UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-CSR

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                         MANAGEMENT INVESTMENT COMPANIES



Investment Company Act file number  811-1629
                                   ------------


                           AXP DIMENSIONS SERIES, INC.
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               (Exact name of registrant as specified in charter)


   50606 AXP Financial Center, Minneapolis, Minnesota                55474
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         (Address of principal executive offices)                 (Zip code)


Leslie L. Ogg - 901 S. Marquette Avenue, Suite 2810, Minneapolis, MN 55402-3268
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                     (Name and address of agent for service)


Registrant's telephone number, including area code:  (612) 330-9283
                                                    -----------------

Date of fiscal year end:     7/31
                         --------------
Date of reporting period:    1/31
                         --------------


AXP(R)
New Dimensions
Fund(R)
                                                               Semiannual Report
                                                            for the Period Ended
                                                                   Jan. 31, 2005

AXP New Dimensions Fund seeks to provide shareholders with long-term growth of
capital.

(logo)                                                                   (logo)
American                                                                AMERICAN
   Express(R)                                                            EXPRESS
 Funds                                                                  (R)


Table of Contents

Fund Snapshot                                                         3

Performance Summary                                                   4

Questions & Answers
   with Portfolio Management                                          5

Investments in Securities                                            11

Financial Statements (Portfolio)                                     15

Notes to Financial Statements (Portfolio)                            18

Financial Statements (Fund)                                          22

Notes to Financial Statements (Fund)                                 26

Fund Expenses Example                                                36

Proxy Voting                                                         38

CORPORATE REORGANIZATION

On Feb. 1, 2005, American Express Company, the parent company of the Fund's
investment manager, American Express Financial Corporation (AEFC), announced
plans to pursue a spin-off of 100% of the common stock of AEFC to shareholders
of American Express Company. The transaction, expected to be completed in the
third quarter of 2005, is subject to certain regulatory and other approvals, as
well as final approval by the board of directors of American Express Company.
Upon completion of the transaction AEFC will be a publicly traded company
separate from American Express Company. The current agreements between the Fund
and AEFC and its affiliates will remain in place. No changes in operations or
personnel, including the portfolio manager of the Fund, are anticipated.

(logo) Dalbar

American Express(R) Funds' reports to shareholders have been awarded the
Communications Seal from Dalbar Inc., an independent financial services research
firm. The Seal recognizes communications demonstrating a level of excellence in
the industry.

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2   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Fund Snapshot
        AT JAN. 31, 2005

PORTFOLIO MANAGERS

Portfolio managers                        Since       Years in industry
Gordon Fines                              1/91               37
Michael Nance                             2/05               12
Trisha Schuster, CFA                      2/05               12

FUND OBJECTIVE

For investors seeking long-term growth of capital.

Inception dates by class
A: 8/1/68     B: 3/20/95   C: 6/26/00   I: 3/4/04    Y: 3/20/95

Ticker symbols by class
A: INNDX      B: INDBX     C: ANDCX     I: ANDIX     Y: IDNYX

Total net assets                                        $13.931 billion

Number of holdings                                                  104

STYLE MATRIX

          STYLE
VALUE     BLEND       GROWTH
                         X      LARGE
                                MEDIUM  SIZE
                                SMALL

Shading within the style matrix indicates areas in which the Fund generally
invests.

SECTOR COMPOSITION

Percentage of portfolio assets

(pie chart)

Technology 20.0%
Consumer discretionary 16.1%
Health care 16.1%
Industrials 12.7%
Financials 11.4%
Energy 9.1%
Short-term securities* 4.7%
Consumer staples 3.6%
Telecommunications 3.1%
Utilities 2.5%
Materials 0.7%

* 0.4% of portfolio assets is due to security lending activity.
  4.3% of portfolio assets is the Portfolio's cash equivalent position.

TOP TEN HOLDINGS

Percentage of portfolio assets

Microsoft (Computer software &  services)                          4.1%
General Electric (Multi-industry)                                  3.9
Citigroup (Finance companies)                                      3.5
UnitedHealth Group (Health care services)                          3.5
Dell (Computer hardware)                                           3.0
Exxon Mobil (Energy)                                               3.0
American Intl Group (Insurance)                                    2.9
Johnson & Johnson (Health care products)                           2.6
Dominion Resources (Utilites -- electric)                          2.5
Target (Retail -- general)                                         2.3

For further detail about these holdings, please refer to the section entitled
"Investments in Securities."

Stock prices of established companies that pay dividends may be less volatile
than the stock market as a whole. There are special risk considerations
associated with international investing related to market, currency, economic,
political and other factors.

Stocks of medium-sized companies may be subject to more abrupt or erratic price
movements than stocks of larger companies. Some of these companies also may have
fewer financial resources.

Fund holdings are subject to change.

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3   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Performance Summary

(bar chart)

                             PERFORMANCE COMPARISON
                     For the six-month period ended Jan. 31, 2005

                    +5.07%              +8.16%          +7.92%

+5.07% = AXP New Dimensions Fund Class A (excluding sales charge)
+8.16% = S&P 500 Index(1) (unmanaged)
+7.92% = Lipper Large-Cap Growth Funds Index(2)

The performance information shown represents past performance and is not a
guarantee of future results. The investment return and principal value of your
investment will fluctuate so that your shares, when redeemed, may be worth more
or less than their original cost. Current performance may be lower or higher
than the performance information shown. You may obtain performance information
current to the most recent month-end by calling (800) 862-7919 or visiting
www.americanexpress.com/funds.

(1)  Standard & Poor's 500 Index (S&P 500 Index), an unmanaged index of common
     stocks, is frequently used as a general measure of market performance. The
     index reflects reinvestment of all distributions and changes in market
     prices, but excludes brokerage commissions or other fees. However, the S&P
     500 companies may be generally larger than those in which the Fund invests.

(2)  The Lipper Large-Cap Growth Funds Index includes the 30 largest large-cap
     growth funds tracked by Lipper Inc. The index's returns include net
     reinvested dividends.

The 5.75% sales charge applicable to Class A shares of the Fund is not reflected
in the bar chart. If reflected, returns would be lower than those shown. The
performance of other classes may vary from that shown because of differences in
expenses.

The indices do not reflect the effects of sales charges, expenses (excluding
Lipper) and taxes.

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4   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers
        WITH PORTFOLIO MANAGEMENT

Below, Portfolio Manager Gordon Fines discusses AXP New Dimensions Fund's
results and positioning for the first half of fiscal year 2005. On Feb. 11,
2005, Michael Nance and Trisha Schuster joined the Fund's portfolio management
team as associate portfolio managers.

Q:  How did the Fund perform for the  six months ended Jan. 31, 2005?

A:  While the period from July 2004 through January 2005 provided positive
    returns for many areas of the U.S. stock market, stocks with very large
    market capitalizations (mega-cap stocks) underperformed amid multiple
    stock-specific events and short-term market trends. AXP New Dimensions
    Fund's Class A shares (excluding sales charge) rose 5.07% for the six months
    ended Jan. 31, 2005 as the Standard & Poor's 500 Index (S&P 500 Index)
    advanced 8.16% for the period.



AVERAGE ANNUAL TOTAL RETURNS
                              Class A                Class B                 Class C          Class I        Class Y
(Inception dates)            (8/1/68)               (3/20/95)               (6/26/00)        (3/4/04)       (3/20/95)
                         NAV(1)    POP(2)      NAV(1)    CDSC(3)       NAV(1)    CDSC(4)      NAV(5)         NAV(6)
at Jan. 31, 2005
                                                                                     
6 months *               +5.07%    -0.97%      +4.67%    +0.67%        +4.62%    +3.62%       +5.28%          +5.18%
1 year                   -0.53%    -6.25%      -1.30%    -5.22%        -1.34%    -1.34%         N/A           -0.36%
3 years                  -0.24%    -2.19%      -1.00%    -1.99%        -1.02%    -1.02%         N/A           -0.06%
5 years                  -4.93%    -6.05%      -5.66%    -5.82%          N/A       N/A          N/A           -4.77%
10 years                +10.24%    +9.59%        N/A       N/A           N/A       N/A          N/A            N/A
Since inception         +11.30%   +11.12%      +8.86%    +8.86%        -7.18%    -7.18%       -1.68%*         +9.86%

at Dec. 31, 2004
6 months *               +3.10%    -2.83%      +2.68%    -2.32%        +2.68%    +1.68%       +3.33%          +3.17%
1 year                   +3.09%    -2.84%      +2.27%    -1.73%        +2.28%    +2.28%         N/A           +3.25%
3 years                  +0.19%    -1.77%      -0.58%    -1.58%        -0.60%    -0.60%         N/A           +0.36%
5 years                  -4.97%    -6.09%      -5.70%    -5.87%          N/A       N/A          N/A           -4.81%
10 years                +10.64%    +9.99%        N/A       N/A           N/A       N/A          N/A            N/A
Since inception         +11.42%   +11.24%      +9.30%    +9.30%        -6.66%    -6.66%       +1.38%*        +10.29%

* Not annualized.


(1)  Excluding sales charge.

(2)  Returns at public offering price (POP) reflect a sales charge of 5.75%.

(3)  Returns at maximum contingent deferred sales charge (CDSC). CDSC applies as
     follows: first year 5%; second and third year 4%; fourth year 3%; fifth
     year 2%; sixth year 1%; no sales charge thereafter.

(4)  1% CDSC applies to redemptions made within the first year of purchase.

(5)  Sales charge is not applicable to these shares. Shares available to
     eligible investors only, currently limited to AXP Portfolio Builder Series
     funds, six affiliated funds-of-funds.

(6)  Sales charge is not applicable to these shares. Shares available to
     institutional investors only.

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5   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers

(begin callout quote)> Our stock selection, specifically in the financials,
consumer staples and industrial sectors, hurt performance. (end callout quote)

    The Lipper Large-Cap Growth Funds Index (Lipper Index), representing the
    Fund's peer group, advanced 7.92% over the same six months.

Q:  What factors affected results?

A:  It was one of the more  disappointing  and difficult  fiscal periods we have
    faced  since  the  early  1990s.  In our  view,  the  main  reasons  for our
    underperformance were:

    o  Our higher-than-S&P 500 Index position in mega-cap stocks. The Fund held
       large positions in mega-cap stocks such as Citigroup, American
       International Group, Pfizer and Wal-Mart, which trailed the overall U.S.
       equity market for the year and the quarter. The Fund had a higher median
       market capitalization and higher weighting in the largest stocks compared
       to its peer group. Some companies such as Pfizer faced product safety
       concerns and increased competition while others faced earnings shortfalls
       or regulatory concerns.

    o  We didn't have enough mid-cap stocks. Mid-cap stocks, which are an
       element of the Fund's S&P 500 Index benchmark, continued to outperform
       large-cap stocks for most of calendar year 2004. This trend began to
       reverse itself toward the end of the year, but the Fund's fiscal period
       results were negatively affected by the market cap of its holdings.

    o  Energy stocks dimmed in the fourth calendar quarter. Energy stock
       performance helped our results for most of the year. However, as the
       price of oil peaked at nearly $55 per barrel in the fourth quarter,
       energy stocks underperformed, and we had a higher-than-S&P 500 Index
       weighting in this sector. We remain positive on the energy sector for the
       year ahead.

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6   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers

(begin callout quote)> Our outlook calls for moderate economic growth and
steadily rising interest rates this year. In our view, this should bode well for
a rotation into high quality, low leverage companies that we favor. (end callout
quote)

    o  Outperformance of value stocks over growth stocks. Value stocks
       significantly outpaced growth stocks in calendar year 2004, as they have
       for several years. We do not believe this style trend can be sustained
       indefinitely. Since the Fund has a distinct and consistent growth focus,
       it was another factor that hurt our short-term results relative to the
       S&P 500 Index, which has both growth and value stocks.

    o  Our stock selection efforts were not as effective as we would have liked.
       Our stock selection, specifically in the financials, consumer staples and
       industrial sectors, hurt performance. One stock that worked well for much
       of the period, eBay, weakened near the end of the period amid earnings
       concerns. For much of the fiscal period, two of the Fund's top 10
       holdings at the start of the fiscal year -- Pfizer and American
       International Group -- did not meet our expectations. Both firms' stock
       prices suffered amid product and regulatory concerns.

    The last few years have been an exceptionally challenging period for
    large-cap growth investors. The current value outperformance cycle, which
    began in 2000, has been longer and deeper than any we've seen over the last
    20 years.

    To illustrate the huge difference in performance between large-cap growth
    and large-cap value stocks in recent years, the chart on page 8 compares the
    returns of the Russell 1000 Growth Index and the Russell 1000 Value Index.
    We firmly believe this imbalance in the equity market will correct itself at
    some point. In this environment, we believe it makes sense for investors to
    maintain their exposure to growth stocks in order to benefit when the market
    again begins to favor growth stocks.

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7   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers

    The Fund's primary benchmark, the S&P 500 Index, contains both growth and
    value stocks. Effective Feb. 11, 2005, we have added the Russell 1000 Growth
    Index as a secondary unmanaged benchmark. We will illustrate the Fund's
    performance against this Russell Index in the Fund's 2005 annual report,
    which will be mailed to you in late September 2005.

COMPARISON OF RETURNS

At Jan. 31, 2005

Growth Stocks, Value Stocks and the S&P 500 Index

                                       1 yr       3 yr    5 yr    10 yr
Russell 1000 Growth Index             +0.70%     -0.71%  -9.04%   +8.99%
Russell 1000 Value Index             +12.45%     +8.20%  +5.59%  +13.28%
S&P 500 Index                         +6.22%     +3.24%  -1.77%  +11.51%

Past performance does not guarantee future results. The Russell 1000(R) Growth
Index is an unmanaged market capitalization weighted index of those Russell 1000
Index companies with higher forecasted growth values The Russell 1000(R) Value
Index is an unmanaged market capitalization weighted index of those Russell 1000
Index companies with lower price-to-book ratios and lower forecasted growth
values. Neither Index figures reflect any deduction for fees or expenses

Q:  Did you have any success stories during the period?

A:  We are pleased to report that some of our holdings finished the period among
    the top performing stocks in the S&P 500 Index. We invested in some
    fast-growing companies whose stock performance helped us. These included
    Starbucks, Apple Computer, Dell Computer and Biogen Idec, to name a few. We
    sought solid, growing businesses with products that had a strong customer
    following and an expanding market share.

    In calendar year 2004, in terms of sector allocation, the Fund had a
    lower-than-S&P 500 Index weighting in health care and consumer discretionary
    stocks and this generally helped us. Large pharmaceutical companies and many
    consumer discretionary stocks did not do well during the fiscal period.

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8   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers

Q:  What portfolio changes did you make and how is the Fund currently
    positioned?

A:  Given their attractive growth characteristics, we have been adding some
    media stocks, including Time Warner and Comcast. We continue to like some of
    the Internet-related companies led by, of course, eBay but also Amazon. We
    also have a small holding in Google. Our largest holdings continue to be
    large-caps such as Microsoft and General Electric. We look for above average
    growth regardless of whether it is mega-cap or large. Currently, we are
    looking for earnings growth above 12%.

    Overall, we emphasize companies that we think are well managed, healthy
    growing companies in terms of balance sheet and income characteristics. We
    try to find companies that show not only earnings growth but also revenue
    growth. Also, in our view, dividend yield and dividend growth are very
    important themes in this market cycle.

Q:  Why was the Fund's management expanded to a team structure?

A:  The addition of two associate portfolio managers provides the Fund with
    additional resources. The Fund's objective to provide shareholders with
    long-term growth of capital remains unchanged.

    Michael Nance brings a consistent and disciplined process of selecting
    growth stocks that provide improved returns, earnings accelerations and
    improved returns on capital. Trisha Schuster provides many years of
    experience in the health care sector, which is one of the largest sectors in
    both the S&P 500 Index and Russell 1000 Growth Index. Mike and Trisha bring
    24 years of combined investment experience to their expanded role,
    experience we believe will add value for shareholders. Mike and Trisha have
    been part of a team supporting this Fund. Both bring ideas that we believe
    can help enhance results.

CHANGES TO TOP TEN HOLDINGS

Jan. 31, 2005 compared to July 31, 2004

Company                                               Change in weighting
Microsoft (Computer software & services)                      Increased
General Electric (Multi-industry)                             No change
Citigroup (Finance companies)                                 Increased
UnitedHealth Group (Health care services)                New to Top Ten
Dell (Computer hardware)                                      Increased
Exxon Mobil (Energy)                                          Decreased
American Intl Group (Insurance)                               Decreased
Johnson & Johnson (Health care products)                 New to Top Ten
Dominion Resources (Utilities -- electric)               New to Top Ten
Target (Retail -- general)                               New to Top Ten

No longer among Top Ten Holdings but still in the portfolio at Jan. 31, 2005
were Amgen, Intel, Pfizer and Wal-Mart Stores. For more information on the Top
Ten Holdings, see this report's Fund Snapshot page or americanexpress.com/funds.

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9   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Questions & Answers

Q:  Has the Fund's investment strategy changed?

A:  No. AXP New  Dimensions  Fund  continues  to be  managed  based on four core
    principles:

    o  Teamwork -- Portfolio managers and a group of dedicated analysts
       constantly exchange individual stock ideas and sector perspectives.

    o  Multifaceted stock selection -- We thoroughly study company fundamentals,
       evaluate company potential to benefit from secular growth themes and
       monitor stock valuations.

    o  Commitment to Research -- In addition to researching company public
       filings, the selection process also incorporates hundreds of company
       visits, industry contacts and external research from third- party
       analysts.

    o  Rigorous Risk Management -- The team actively manages and monitors the
       portfolio's risk profile.

Q:  How do you intend to manage the Fund in the coming months?

A:  We remain upbeat about the prospects for the Fund in 2005. Our outlook calls
    for moderate economic growth and steadily rising interest rates this year.
    In our view, this should bode well for a rotation into high-quality
    low-leverage companies that we favor. Relative valuations also suggest that
    a rotation toward larger cap companies is probably overdue.

    Our experience has taught us that during periods of rising interest rates
    and slowing economic growth, when corporate earnings are nearing a peak,
    higher quality companies generally perform better than lower quality
    companies. In fact, a shift in market emphasis toward quality growth
    companies with sound balance sheets --the kind of companies that dominate
    the Fund's portfolio -- will provide an excellent opportunity for the Fund
    to regain ground. We express our gratitude for shareholders' patience, and
    we are optimistic that investors who have expressed long-term confidence in
    our strategy will be rewarded in 2005.

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10   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Investments in Securities

Growth Trends Portfolio

Jan. 31, 2005 (Unaudited)

(Percentages represent value of investments compared to net assets)

Common stocks (95.3%)
Issuer                                         Shares                 Value(a)

Aerospace & defense (3.1%)
Lockheed Martin                             2,500,000            $144,525,000
Northrop Grumman                            2,500,000             129,700,000
United Technologies                         1,500,000             151,020,000
Total                                                             425,245,000

Banks and savings & loans (1.6%)
Bank of America                             4,700,000             217,939,000

Beverages & tobacco (1.7%)
PepsiCo                                     4,500,000             241,650,000

Broker dealers (0.6%)
Charles Schwab                              7,305,500              82,113,820

Cable (1.1%)
Comcast Special Cl A                        5,000,000(b)          158,050,000

Cellular telecommunications (0.6%)
Vodafone Group ADR                          3,000,000(c)           77,940,000

Chemicals (0.7%)
EI du Pont de Nemours & Co                  2,000,000              95,120,000

Computer hardware (7.6%)
Apple Computer                              3,000,000(b)          230,700,000
Cisco Systems                              10,000,000(b)          180,400,000
Dell                                       10,000,000(b)          417,600,000
EMC                                        18,000,000(b)          235,800,000
Total                                                           1,064,500,000

Computer software & services (9.2%)
Google Cl A                                   200,000(b,d)         39,126,000
Intl Business Machines                      2,500,000             233,550,000
Juniper Networks                            8,000,000(b)          201,040,000
Microsoft                                  22,000,000             578,160,000
SAP ADR                                     3,400,000(c)          131,648,000
Symantec                                    4,000,000(b)           93,400,000
Total                                                           1,276,924,000

Electronics (3.2%)
Applied Materials                           4,000,000(b)           63,600,000
Intel                                       4,000,000              89,800,000
Samsung Electronics                           400,000(c)          193,024,771
Texas Instruments                           2,000,000              46,420,000
Xerox                                       3,000,000(b)           47,640,000
Total                                                             440,484,771

Energy (6.5%)
Apache                                      3,000,000             163,260,000
ChevronTexaco                               2,900,000             157,760,000
ConocoPhillips                              1,800,000             167,022,000
Exxon Mobil                                 8,000,000             412,800,000
Total                                                             900,842,000

Energy equipment & services (2.6%)
Halliburton                                 3,500,000             143,955,000
Schlumberger                                2,000,000             136,080,000
Transocean                                  2,000,000(b)           88,000,000
Total                                                             368,035,000

Environmental services (--%)
Waste Management                               66,700               1,934,300

Finance companies (3.5%)
Citigroup                                  10,000,000             490,500,000

Financial services (2.3%)
Goldman Sachs Group                         1,000,000             107,850,000
MBNA                                        3,800,000             101,004,000
SLM                                         2,200,000(d)          110,418,000
Total                                                             319,272,000

See accompanying notes to investments in securities.
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11   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Common stocks (continued)
Issuer                                         Shares                 Value(a)

Health care products (12.6%)
Abbott Laboratories                         2,500,000            $112,550,000
Amgen                                       3,500,000(b)          217,840,000
Biogen Idec                                 3,000,000(b)          194,880,000
Boston Scientific                           4,500,000(b)          148,770,000
Eli Lilly & Co                              1,000,000              54,240,000
Forest Laboratories                            71,900(b)            2,986,007
Gilead Sciences                             3,000,000(b)           99,300,000
Johnson & Johnson                           5,500,000  (d)        355,850,000
Medtronic                                   2,000,000             104,980,000
Novartis ADR                                1,500,000(c)           71,820,000
Pfizer                                      8,000,000             193,280,000
St. Jude Medical                            3,000,000(b)          117,840,000
Zimmer Holdings                             1,080,800(b)           85,221,080
Total                                                           1,759,557,087

Health care services (3.5%)
UnitedHealth Group                          5,500,000             488,950,000

Home building (0.3%)
Pulte Homes                                   600,000              39,648,000

Household products (1.9%)
Procter & Gamble                            5,000,000             266,150,000

Industrial transportation (1.2%)
United Parcel Service Cl B                  2,200,000             164,296,000

Insurance (3.4%)
AFLAC                                       1,000,000              39,510,000
American Intl Group                         6,000,000             397,740,000
UnumProvident                               2,000,000              34,340,000
Total                                                             471,590,000

Leisure time & entertainment (1.2%)
Carnival                                    3,000,000  (d)        172,800,000

Lodging & gaming (0.4%)
Intl Game Technology                        2,000,000              62,600,000

Machinery (1.5%)
Deere & Co                                  3,000,000             208,290,000

Media (4.7%)
Amazon.com                                    800,000(b)           34,576,000
eBay                                        2,500,000(b)          203,750,000
Time Warner                                15,000,000(b)          270,000,000
Yahoo!                                      4,200,000(b)          147,882,000
Total                                                             656,208,000

Multi-industry (7.0%)
3M                                          3,000,000             253,080,000
General Electric                           15,000,000             541,950,000
Tyco Intl                                   4,800,000(c)          173,472,000
Total                                                             968,502,000

Restaurants (2.0%)
McDonald's                                  4,500,000             145,755,000
Starbucks                                   2,500,000(b)          135,000,000
Total                                                             280,755,000

Retail -- general (6.2%)
Best Buy                                      700,000              37,653,000
Home Depot                                  3,400,000             140,284,000
Staples                                     1,800,000(d)           58,932,000
Target                                      6,200,000             314,774,000
Wal-Mart Stores                             6,000,000             314,400,000
Total                                                             866,043,000

Telecom equipment & services (2.6%)
Motorola                                    4,000,000              62,960,000
QUALCOMM                                    8,000,000             297,920,000
Total                                                             360,880,000

Utilities -- electric (2.5%)
Dominion Resources                          5,000,000             346,900,000

Total common stocks
(Cost: $11,686,579,462)                                       $13,273,718,978

See accompanying notes to investments in securities.
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12   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Short-term securities (4.7%)(e)
Issuer                  Effective           Amount                  Value(a)
                          yield           payable at
                                           maturity

U.S. government agencies (0.7%)
Federal Home Loan Bank Disc Nt
  02-18-05                2.33%           $25,000,000             $24,970,875
Federal Natl Mtge Assn Disc Nts
  02-01-05                2.27              4,400,000               4,399,723
  02-09-05                2.25             50,000,000              49,971,874
  02-16-05                2.32             17,800,000              17,781,646
Total                                                              97,124,118

Commercial paper (4.0%)
Amsterdam Funding
  02-11-05                2.33             24,750,000              24,732,379
BNP Paribas
  02-01-05                2.49              4,650,000               4,649,678
Barton Capital LLC
  02-08-05                2.31             10,400,000              10,394,661
Beta Finance
  02-08-05                2.33             25,000,000              24,987,055
  04-29-05                2.55              5,500,000               5,465,973
CHARTA LLC
  04-25-05                2.54             15,000,000              14,911,467
CRC Funding LLC
  02-17-05                2.35              3,000,000               2,996,671
Credit Suisse First Boston NY
  02-03-05                2.30             30,000,000              29,994,251
Danske
  02-14-05                2.36             10,000,000               9,990,822
Delaware Funding LLC
  02-07-05                2.30             20,000,000              19,991,056
  02-15-05                2.34             50,000,000              49,951,250
  03-01-05                2.51             25,000,000              24,949,653
General Electric Capital
  02-01-05                2.48              7,700,000               7,699,470
Jupiter Securitization
  02-22-05                2.45             30,000,000              29,955,084
Kitty Hawk Funding
  02-23-05                2.50             25,000,000              24,960,069
Morgan Stanley
  02-04-05                2.48             12,000,000              11,996,693
  02-14-05                2.53             50,000,000              49,950,806
Old Line Funding LLC
  03-03-05                2.51             39,831,000              39,745,252
Park Avenue Receivables
  02-10-05                2.33             40,000,000              39,974,110
  02-25-05                2.49             30,000,000              29,948,126
Ranger Funding LLC
  02-24-05                2.48             30,000,000              29,950,400
Sheffield Receivables
  02-01-05                2.50              6,350,000               6,349,559
Variable Funding Capital
  02-11-05                2.33             18,600,000              18,586,757
  03-04-05                2.52             50,000,000              49,888,444
Total                                                             562,019,686

Total short-term securities
(Cost: $659,182,049)                                             $659,143,804

Total investments in securities
(Cost: $12,345,761,511)(f)                                    $13,932,862,782

See accompanying notes to investments in securities.

- --------------------------------------------------------------------------------
13   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Notes to investments in securities

(a)    Securities are valued by procedures described in Note 1 to the financial
       statements.

(b)    Non-income producing.

(c)    Foreign security values are stated in U.S. dollars. At Jan. 31, 2005, the
       value of foreign securities represented 4.6% of net assets.

(d)    At Jan. 31, 2005, security was partially or fully on loan. See Note 4 to
       the financial statements.

(e)    Cash collateral received from security lending activity is invested in
       short-term securities and represents 0.4% of net assets. See Note 5 to
       the financial statements. 4.3% of net assets is the Portfolio's cash
       equivalent position.

(f)    At Jan. 31, 2005, the cost of securities for federal income tax purposes
       was approximately $12,345,762,000 and the approximate aggregate gross
       unrealized appreciation and depreciation based on that cost was:

       Unrealized appreciation                                 $2,026,191,000
       Unrealized depreciation                                   (439,090,000)
                                                                 ------------
       Net unrealized appreciation                             $1,587,101,000
                                                               --------------

How to find information about the Fund's portfolio holdings

(i)    The Fund files its complete schedule of portfolio holdings with the
       Securities and Exchange Commission (Commission) for the first and third
       quarters of each fiscal year on Form N-Q;

(ii)   The Fund's Forms N-Q are available on the Commission's website at
       http://www.sec.gov;

(iii)  The Fund's Forms N-Q may be reviewed and copied at the Commission's
       Public Reference Room in Washington, DC (information on the operations of
       the Public Reference Room may be obtained by calling 1-800-SEC-0330); and

(iv)   The Fund's complete schedule of portfolio holdings, as disclosed in its
       annual and semiannual shareholder reports and in its filings on Form N-Q,
       can be found at www.americanexpress.com/funds.

- --------------------------------------------------------------------------------
14   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Financial Statements



Statement of assets and liabilities
Growth Trends Porfolio

Jan. 31, 2005 (Unaudited)
Assets
Investments in securities, at value (Note 1)*

                                                                        
   (identified cost $12,345,761,511)                                       $13,932,862,782
Foreign currency holdings (identified cost $5,521) (Note 1)                          6,049
Dividends and accrued interest receivable                                        7,118,492
Receivable for investment securities sold                                      151,095,223
                                                                               -----------
Total assets                                                                14,091,082,546
                                                                            --------------
Liabilities
Disbursements in excess of cash on demand deposit                                4,093,349
Payable for investment securities purchased                                     92,416,540
Payable upon return of securities loaned (Note 4)                               58,600,770
Accrued investment management services fee                                         591,411
Other accrued expenses                                                             434,286
                                                                                   -------
Total liabilities                                                              156,136,356
                                                                               -----------
Net assets                                                                 $13,934,946,190
                                                                           ===============
* Including securities on loan, at value (Note 4)                          $    58,061,539
                                                                           ---------------


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
15   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Statement of operations
Growth Trends Porfolio

Six months ended Jan. 31, 2005 (Unaudited)
Investment income
Income:
                                                                           
Dividends                                                                     $149,979,553
Interest                                                                         6,071,541
Fee income from securities lending (Note 4)                                        104,054
   Less foreign taxes withheld                                                    (246,353)
                                                                                  --------
Total income                                                                   155,908,795
                                                                               -----------
Expenses (Note 2):
Investment management services fee                                              34,802,763
Compensation of board members                                                       29,069
Custodian fees                                                                     571,405
Audit fees                                                                          18,000
Other                                                                              274,995
                                                                                   -------
Total expenses                                                                  35,696,232
   Earnings credits on cash balances (Note 2)                                         (719)
                                                                                      ----
Total net expenses                                                              35,695,513
                                                                                ----------
Investment income (loss) -- net                                                120,213,282
                                                                               -----------
Realized and unrealized gain (loss) -- net
Net realized gain (loss) on:
   Security transactions (Note 3)                                              396,634,385
   Foreign currency transactions                                                  (169,253)
   Futures contracts                                                            (1,726,848)
                                                                                ----------
Net realized gain (loss) on investments                                        394,738,284
Net change in unrealized appreciation (depreciation) on investments
   and on translation of assets and liabilities in foreign currencies          267,652,761
                                                                               -----------
Net gain (loss) on investments and foreign currencies                          662,391,045
                                                                               -----------
Net increase (decrease) in net assets resulting from operations               $782,604,327
                                                                              ============


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
16   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Statements of changes in net assets
Growth Trends Porfolio
                                                                                   Jan. 31, 2005             July 31, 2004
                                                                                 Six months ended              Year ended
                                                                                    (Unaudited)
Operations
                                                                                                      
Investment income (loss) -- net                                                   $   120,213,282           $   153,163,075
Net realized gain (loss) on investments                                               394,738,284             1,326,193,728
Net change in unrealized appreciation (depreciation) on investments
   and on translation of assets and liabilities in foreign currencies                 267,652,761              (740,840,157)
                                                                                      -----------              ------------
Net increase (decrease) in net assets resulting from operations                       782,604,327               738,516,646
                                                                                      -----------               -----------
Proceeds from contributions                                                            56,873,827               588,788,643
Fair value of withdrawals                                                          (2,224,936,120)           (3,075,163,840)
In-kind contributions in connection with fund mergers (Note 1)                                 --               221,872,382
                                                                                   --------------            --------------
Net contributions (withdrawals) from partners                                      (2,168,062,293)           (2,264,502,815)
                                                                                   --------------            --------------
Total increase (decrease) in net assets                                            (1,385,457,966)           (1,525,986,169)
Net assets at beginning of period                                                  15,320,404,156            16,846,390,325
                                                                                   --------------            --------------
Net assets at end of period                                                       $13,934,946,190           $15,320,404,156
                                                                                  ===============           ===============


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
17   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Notes to Financial Statements

Growth Trends Portfolio

(Unaudited as to Jan. 31, 2005)

1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

Growth Trends Portfolio (the Portfolio) is a series of Growth Trust (the Trust)
and is registered under the Investment Company Act of 1940 (as amended) as a
diversified, open-end management investment company. Growth Trends Portfolio
invests primarily in common stocks of companies showing potential for
significant growth and operating in areas where economic or technological
changes are occurring. The Declaration of Trust permits the Trustees to issue
non-transferable interests in the Portfolio.

On June 25, 2004, AXP New Dimensions Fund acquired the assets and assumed the
identified liabilities of AXP Focused Growth Fund and AXP Growth Dimensions
Fund. Upon receipt of these assets and liabilities, AXP New Dimensions Fund made
an in-kind contribution of $221,872,382 to Growth Trends Portfolio.

The Portfolio's significant accounting policies are summarized below:

Use of estimates

Preparing financial statements that conform to accounting principles generally
accepted in the United States of America requires management to make estimates
(e.g., on assets, liabilities and contingent assets and liabilities) that could
differ from actual results.

Valuation of securities

All securities are valued at the close of each business day. Securities traded
on national securities exchanges or included in national market systems are
valued at the last quoted sales price. Debt securities are generally traded in
the over-the-counter market and are valued at a price that reflects fair value
as quoted by dealers in these securities or by an independent pricing service.
Pursuant to procedures adopted by the Board of Trustees of the portfolios,
American Express Financial Corporation (AEFC) utilizes Fair Value Pricing (FVP).
FVP determinations are made in good faith in accordance with these procedures.
If a development or event is so significant that there is a reasonably high
degree of certainty that the effect of the development or event has actually
caused the closing price to no longer reflect the actual value, the closing
prices, as determined at the close of the applicable foreign market, may be
adjusted to reflect the fair value of the affected foreign securities as of the
close of the New York Stock Exchange. Significant events include material
movements in the U.S. securities markets prior to the opening of foreign markets
on the following trading day. FVP results in an estimated price that reasonably
reflects the current market conditions in order to value the portfolio holdings
such that shareholder transactions receive a fair net asset value (NAV).
Short-term securities maturing in more than 60 days from the valuation date are
valued at the market price or approximate market value based on current interest
rates; those maturing in 60 days or less are valued at amortized cost.

- --------------------------------------------------------------------------------
18   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Option transactions

To produce incremental earnings, protect gains and facilitate buying and selling
of securities for investments, the Portfolio may buy and write options traded on
any U.S. or foreign exchange or in the over-the-counter market where completing
the obligation depends upon the credit standing of the other party. The
Portfolio also may buy and sell put and call options and write covered call
options on portfolio securities as well as write cash-secured put options. The
risk in writing a call option is that the Portfolio gives up the opportunity for
profit if the market price of the security increases. The risk in writing a put
option is that the Portfolio may incur a loss if the market price of the
security decreases and the option is exercised. The risk in buying an option is
that the Portfolio pays a premium whether or not the option is exercised. The
Portfolio also has the additional risk of being unable to enter into a closing
transaction if a liquid secondary market does not exist.

Option contracts are valued daily at the closing prices on their primary
exchanges and unrealized appreciation or depreciation is recorded. The Portfolio
will realize a gain or loss when the option transaction expires or closes. When
an option is exercised, the proceeds on sales for a written call option, the
purchase cost for a written put option or the cost of a security for a purchased
put or call option is adjusted by the amount of premium received or paid.

Futures transactions

To gain exposure to or protect itself from market changes, the Portfolio may buy
and sell financial futures contracts traded on any U.S. or foreign exchange. The
Portfolio also may buy and write put and call options on these futures
contracts. Risks of entering into futures contracts and related options include
the possibility of an illiquid market and that a change in the value of the
contract or option may not correlate with changes in the value of the underlying
securities.

Upon entering into a futures contract, the Portfolio is required to deposit
either cash or securities in an amount (initial margin) equal to a certain
percentage of the contract value. Subsequent payments (variation margin) are
made or received by the Portfolio each day. The variation margin payments are
equal to the daily changes in the contract value and are recorded as unrealized
gains and losses. The Portfolio recognizes a realized gain or loss when the
contract is closed or expires.

Foreign currency translations and foreign currency contracts

Securities and other assets and liabilities denominated in foreign currencies
are translated daily into U.S. dollars. Foreign currency amounts related to the
purchase or sale of securities and income and expenses are translated at the
exchange rate on the transaction date. The effect of changes in foreign exchange
rates on realized and unrealized security gains or losses is reflected as a
component of such gains or losses. In the statement of operations, net realized
gains or losses from foreign currency transactions, if any, may arise from sales
of foreign currency, closed forward contracts, exchange gains or losses realized
between the trade date and settlement date on securities transactions, and other
translation gains or losses on dividends, interest income and foreign
withholding taxes. At Jan. 31, 2005, foreign currency holdings were entirely
comprised of Taiwan Dollars.

- --------------------------------------------------------------------------------
19   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


The Portfolio may enter into forward foreign currency exchange contracts for
operational purposes and to protect against adverse exchange rate fluctuation.
The net U.S. dollar value of foreign currency underlying all contractual
commitments held by the Portfolio and the resulting unrealized appreciation or
depreciation are determined using foreign currency exchange rates from an
independent pricing service. The Portfolio is subject to the credit risk that
the other party will not complete its contract obligations.

Guarantees and indemnifications

Under the Portfolio's organizational documents, its officers and trustees are
indemnified against certain liabilities arising out of the performance of their
duties to the Portfolio. In addition, certain of the Portfolio's contracts with
its service providers contain general indemnification clauses. The Portfolio's
maximum exposure under these arrangements is unknown since the amount of any
future claims that may be made against the Portfolio cannot be determined and
the Portfolio has no historical basis for predicting the likelihood of any such
claims.

Federal taxes

For federal income tax purposes the Portfolio qualifies as a partnership and
each investor in the Portfolio is treated as the owner of its proportionate
share of the net assets, income, expenses and realized and unrealized gains and
losses of the Portfolio. As a "pass-through" entity, the Portfolio therefore
does not pay any income dividends or capital gain distributions.

Other

Security transactions are accounted for on the date securities are purchased or
sold. Dividend income is recognized on the ex-dividend date and interest income,
including amortization of premium, market discount and original issue discount
using the effective interest method, is accrued daily.

2. FEES AND EXPENSES

The Trust, on behalf of the Portfolio, has an Investment Management Services
Agreement with AEFC to manage its portfolio. Under this agreement, AEFC
determines which securities will be purchased, held or sold. The management fee
is a percentage of the Portfolio's average daily net assets that declines from
0.6% to 0.48% annually as the Portfolio's assets increase. The fee may be
adjusted upward or downward by a performance incentive adjustment based on a
comparison of the performance of Class A shares of AXP New Dimensions Fund to
the Lipper Large-Cap Growth Funds Index. In certain circumstances, the board may
approve a change in the index. The maximum adjustment is 0.12% per year. If the
performance difference is less than 0.50%, the adjustment will be zero. The
adjustment decreased the fee by $4,051,820 for the six months ended Jan. 31,
2005.

Under the agreement, the Trust also pays taxes, brokerage commissions and
nonadvisory expenses, which include custodian fees, audit and certain legal
fees, fidelity bond premiums, registration fees for units, office expenses,
consultants' fees, compensation of trustees, corporate filing fees, expenses
incurred in connection with lending securities of the Portfolio and any other
expenses properly payable by the Trust or Portfolio and approved by the board.

- --------------------------------------------------------------------------------
20   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Under a Deferred Compensation Plan (the Plan), non-interested trustees may defer
receipt of their compensation. Deferred amounts are treated as though equivalent
dollar amounts had been invested in shares of the underlying Fund or other
American Express mutual funds. The Portfolio's liability for these amounts is
adjusted for market value changes and remains in the Portfolio until distributed
in accordance with the Plan.

During the six months ended Jan. 31, 2005, the Portfolio's custodian fees were
reduced by $719 as a result of earnings credits from overnight cash balances.
The Portfolio also pays custodian fees to American Express Trust Company, an
affiliate of AEFC.

According to a Placement Agency Agreement, American Express Financial Advisors
Inc. acts as placement agent of the Trust's units.

3. SECURITIES TRANSACTIONS

Cost of purchases and proceeds from sales of securities (other than short-term
obligations) aggregated $4,567,608,312 and $6,632,507,511, respectively, for the
six months ended Jan. 31, 2005. Realized gains and losses are determined on an
identified cost basis.

Brokerage clearing fees paid to brokers affiliated with AEFC were $108,435 for
the six months ended Jan. 31, 2005.

4. LENDING OF PORTFOLIO SECURITIES

At Jan. 31, 2005, securities valued at $58,061,539 were on loan to brokers. For
collateral, the Portfolio received $58,600,770 in cash. Cash collateral received
is invested in short-term securities, which are included in the short-term
section of the "Investments in securities." Income from securities lending
amounted to $104,054 for the six months ended Jan. 31, 2005. The risks to the
Portfolio of securities lending are that the borrower may not provide additional
collateral when required or return the securities when due.

5. FINANCIAL HIGHLIGHTS

The table below shows certain important financial information for evaluating the
Portfolio's results.



Ratios/supplemental data
Fiscal period ended July 31,                                             2005(e)      2004       2003       2002       2001
                                                                                                     
Ratio of expenses to average daily net assets(a)                         .48%(b)      .45%       .58%       .61%       .59%
Ratio of net investment income (loss) to average daily net assets       1.60%(b)      .91%       .92%       .64%       .52%
Portfolio turnover rate (excluding short-term securities)                 32%          49%        20%        27%        29%
Total return(c)                                                         5.30%(d)     4.05%     10.01%    (20.76%)   (20.77%)


(a)  Expense ratio is based on total expenses of the Portfolio before reduction
     of earnings credits on cash balances. The ratio does not include feeder
     fund expenses.

(b)  Adjusted to an annual basis.

(c)  Total return is based on a calculated Portfolio NAV and does not reflect
     payment of a sales charge.

(d)  Not annualized.

(e)  Six months ended Jan. 31, 2005 (Unaudited).

- --------------------------------------------------------------------------------
21   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Financial Statements



Statement of assests and liabilities
AXP New Dimensions Fund

Jan. 31, 2005
Assets
                                                                                                      
Investment in Portfolio (Note 1)                                                                            $13,934,873,513
Capital shares receivable                                                                                         1,573,809
                                                                                                                  ---------
Total assets                                                                                                 13,936,447,322
                                                                                                             --------------
Liabilities
Capital shares payable                                                                                            4,159,804
Accrued distribution fee                                                                                            385,309
Accrued service fee                                                                                                  22,978
Accrued transfer agency fee                                                                                         186,462
Accrued administrative services fee                                                                                  38,259
Other accrued expenses                                                                                              623,134
                                                                                                                    -------
Total liabilities                                                                                                 5,415,946
                                                                                                                  ---------
Net assets applicable to outstanding capital stock                                                          $13,931,031,376
                                                                                                            ===============
Represented by
Capital stock -- $.01 par value (Note 1)                                                                    $     6,013,206
Additional paid-in capital                                                                                   12,039,707,545
Excess of distributions over net investment income                                                               (5,641,266)
Accumulated net realized gain (loss) (Note 5)                                                                   303,830,610
Unrealized appreciation (depreciation) on investments
   and on translation of assets and liabilities in foreign currencies                                         1,587,121,281
                                                                                                              -------------
Total -- representing net assets applicable to outstanding capital stock                                    $13,931,031,376
                                                                                                            ===============
Net assets applicable to outstanding shares:               Class A                                          $ 8,432,978,506
                                                           Class B                                          $ 2,559,551,128
                                                           Class C                                          $    57,824,102
                                                           Class I                                          $    59,489,881
                                                           Class Y                                          $ 2,821,187,759
Net asset value per share of outstanding capital stock:    Class A shares             360,580,067           $         23.39
                                                           Class B shares             115,522,878           $         22.16
                                                           Class C shares               2,612,972           $         22.13
                                                           Class I shares               2,533,686           $         23.48
                                                           Class Y shares             120,070,968           $         23.50
                                                                                      -----------           ---------------


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
22   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Statement of operations
AXP New Dimensions Fund

Six months ended Jan. 31, 2005 (Unaudited)
Investment income
Income:
                                                                           
Dividends                                                                     $149,978,831
Interest                                                                         6,074,775
Fee income from securities lending                                                 104,053
   Less foreign taxes withheld                                                    (246,352)
                                                                                  --------
Total income                                                                   155,911,307
                                                                               -----------
Expenses (Note 2):
Expenses allocated from Portfolio                                               35,695,345
Distribution fee
   Class A                                                                      11,368,457
   Class B                                                                      13,879,321
   Class C                                                                         309,850
Transfer agency fee                                                             12,070,512
Incremental transfer agency fee
   Class A                                                                         740,608
   Class B                                                                         552,698
   Class C                                                                          14,449
Service fee -- Class Y                                                           1,506,797
Administrative services fees and expenses                                        2,569,654
Compensation of board members                                                       15,952
Printing and postage                                                             1,627,659
Registration fees                                                                   31,118
Audit fees                                                                           6,000
Other                                                                               87,869
                                                                                    ------
Total expenses                                                                  80,476,289
   Earnings credits on cash balances (Note 2)                                     (157,139)
                                                                                  --------
Total net expenses                                                              80,319,150
                                                                                ----------
Investment income (loss) -- net                                                 75,592,157
                                                                                ----------
Realized and unrealized gain (loss) -- net
Net realized gain (loss) on:
   Security transactions                                                       396,633,129
   Foreign currency transactions                                                  (169,252)
   Futures contracts                                                            (1,726,848)
                                                                                ----------
Net realized gain (loss) on investments                                        394,737,029
Net change in unrealized appreciation (depreciation) on investments
   and on translation of assets and liabilities in foreign currencies          267,650,927
                                                                               -----------
Net gain (loss) on investments and foreign currencies                          662,387,956
                                                                               -----------
Net increase (decrease) in net assets resulting from operations               $737,980,113
                                                                              ============


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
23   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Statements of changes in net assets
AXP New Dimensions Fund
                                                                                       Jan. 31, 2005           July 31, 2004
                                                                                     Six months ended            Year ended
                                                                                        (Unaudited)
Operations and distributions
                                                                                                       
Investment income (loss) -- net                                                     $  75,592,157            $   53,646,007
Net realized gain (loss) on investments                                               394,737,029             1,326,188,766
Net change in unrealized appreciation (depreciation) on investments
   and on translation of assets and liabilities in foreign currencies                 267,650,927              (740,837,241)
                                                                                      -----------              ------------
Net increase (decrease) in net assets resulting from operations                       737,980,113               638,997,532
                                                                                      -----------               -----------
Distributions to shareholders from:
   Net investment income
      Class A                                                                         (59,842,681)              (46,364,316)
      Class I                                                                            (402,755)                  (24,173)
      Class Y                                                                         (25,264,241)              (22,183,807)
   Net realized gain
      Class A                                                                         (66,369,513)                       --
      Class B                                                                         (21,459,288)                       --
      Class C                                                                            (480,445)                       --
      Class I                                                                            (279,703)                       --
      Class Y                                                                         (22,415,431)                       --
                                                                                     ------------               -----------
Total distributions                                                                  (196,514,057)              (68,572,296)
                                                                                     ------------               -----------


- --------------------------------------------------------------------------------
24   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Statements of changes in net assets (continued)
AXP New Dimensions Fund
                                                                                       Jan. 31, 2005            July 31, 2004
                                                                                     Six months ended            Year ended
                                                                                        (Unaudited)
Capital share transactions (Note 3)
Proceeds from sales
                                                                                                   
   Class A shares (Note 2)                                                        $   179,214,050           $   957,437,754
   Class B shares                                                                      76,158,426               289,864,944
   Class C shares                                                                       4,122,016                15,172,920
   Class I shares                                                                      40,269,455                18,590,210
   Class Y shares                                                                     150,823,692               649,466,427
Fund merger (Note 6)
   Class A shares                                                                              --               145,036,482
   Class B shares                                                                              --                71,825,421
   Class C shares                                                                              --                 4,985,482
   Class Y shares                                                                              --                    24,997
Reinvestment of distributions at net asset value
   Class A shares                                                                     122,901,165                45,072,267
   Class B shares                                                                      21,267,536                        --
   Class C shares                                                                         472,648                        --
   Class I shares                                                                         682,371                    24,152
   Class Y shares                                                                      46,516,684                21,742,867
Payments for redemptions
   Class A shares                                                                  (1,515,369,973)           (2,032,028,533)
   Class B shares (Note 2)                                                           (492,858,042)           (1,071,801,488)
   Class C shares (Note 2)                                                            (12,444,726)              (17,016,745)
   Class I shares                                                                        (121,799)                  (10,876)
   Class Y shares                                                                    (549,980,254)           (1,196,861,524)
                                                                                     ------------            --------------
Increase (decrease) in net assets from capital share transactions                  (1,928,346,751)           (2,098,475,243)
                                                                                   --------------            --------------
Total increase (decrease) in net assets                                            (1,386,880,695)           (1,528,050,007)
Net assets at beginning of period                                                  15,317,912,071            16,845,962,078
                                                                                   --------------            --------------
Net assets at end of period                                                       $13,931,031,376           $15,317,912,071
                                                                                  ===============           ===============
Undistributed (excess of distributions over) net investment income                $    (5,641,266)          $     4,276,254
                                                                                  ---------------           ---------------


See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
25   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Notes to Financial Statements

AXP New Dimensions Fund

(Unaudited as to Jan. 31, 2005)

1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

The Fund is a series of AXP Dimensions Series, Inc. and is registered under the
Investment Company Act of 1940 (as amended) as a diversified, open-end
management investment company. AXP Dimensions Series, Inc. has 10 billion
authorized shares of capital stock that can be allocated among the separate
series as designated by the board.

The Fund offers Class A, Class B, Class C and Class Y shares.

o   Class A shares are sold with a front-end sales charge.

o   Class B shares may be subject to a contingent  deferred  sales charge (CDSC)
    and  automatically  convert to Class A shares during the ninth calendar year
    of ownership.

o   Class C shares may be subject to a CDSC.

o   Class Y shares  have no sales  charge  and are  offered  only to  qualifying
    institutional investors.

The Fund offers an additional class of shares, Class I, exclusively to certain
institutional investors. Class I shares have no sales charge and are made
available through a separate prospectus supplement provided to investors
eligible to purchase the shares. At Jan. 31, 2005, AEFC and the AXP Portfolio
Builder Series funds owned 100% of Class I shares, which represents 0.43% of the
Fund's net assets.

All classes of shares have identical voting, dividend and liquidation rights.
The distribution fee, transfer agency fees and service fee (class specific
expenses) differ among classes. Income, expenses (other than class specific
expenses) and realized and unrealized gains or losses on investments are
allocated to each class of shares based upon its relative net assets.

Investment in Growth Trends Portfolio

The Fund invests all of its assets in the Growth Trends Portfolio (the
Portfolio), a series of Growth Trust (the Trust), an open-end investment company
that has the same objectives as the Fund. The Portfolio invests primarily in
common stocks of companies showing potential for significant growth and
operating in areas where economic or technological changes are occurring.

The Fund records daily its share of the Portfolio's income, expenses and
realized and unrealized gains and losses. The financial statements of the
Portfolio are included elsewhere in this report and should be read in
conjunction with the Fund's financial statements.

The Fund records its investment in the Portfolio at the value that is equal to
the Fund's proportionate ownership interest in the Portfolio's net assets. The
percentage of the Portfolio owned by the Fund at Jan. 31, 2005 was 99.99%.

All securities held by the Portfolio are valued at the close of each business
day. Securities traded on national securities exchanges or included in national
market systems are valued at the last quoted sales price. Debt securities are
generally traded in the over-the-counter market and are valued at a price that
reflects fair value as quoted by dealers in these securities or by

- --------------------------------------------------------------------------------
26   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


an independent pricing service. Pursuant to procedures adopted by the Board of
Trustees of the portfolios, AEFC utilizes Fair Value Pricing (FVP). FVP
determinations are made in good faith in accordance with these procedures. If a
development or event is so significant that there is a reasonably high degree of
certainty that the effect of the development or event has actually caused the
closing price to no longer reflect the actual value, the closing prices, as
determined at the close of the applicable foreign market, may be adjusted to
reflect the fair value of the affected foreign securities as of the close of the
New York Stock Exchange. Significant events include material movements in the
U.S. securities markets prior to the opening of foreign markets on the following
trading day. FVP results in an estimated price that reasonably reflects the
current market conditions in order to value the portfolio holdings such that
shareholder transactions receive a fair NAV. Short-term securities maturing in
more than 60 days from the valuation date are valued at the market price or
approximate market value based on current interest rates; those maturing in 60
days or less are valued at amortized cost.

Use of estimates

Preparing financial statements that conform to accounting principles generally
accepted in the United States of America requires management to make estimates
(e.g., on assets, liabilities and contingent assets and liabilities) that could
differ from actual results.

Guarantees and indemnifications

Under the Fund's organizational documents, its officers and directors are
indemnified against certain liabilities arising out of the performance of their
duties to the Fund. In addition, certain of the Fund's contracts with its
service providers contain general indemnification clauses. The Fund's maximum
exposure under these arrangements is unknown since the amount of any future
claims that may be made against the Fund cannot be determined and the Fund has
no historical basis for predicting the likelihood of any such claims.

Federal taxes

The Fund's policy is to comply with all sections of the Internal Revenue Code
that apply to regulated investment companies and to distribute substantially all
of its taxable income to shareholders. No provision for income or excise taxes
is thus required.

Net investment income (loss) and net realized gains (losses) may differ for
financial statement and tax purposes primarily because of deferred losses on
certain futures contracts, the recognition of certain foreign currency gains
(losses) as ordinary income (loss) for tax purposes, and losses deferred due to
"wash sale" transactions. The character of distributions made during the year
from net investment income or net realized gains may differ from their ultimate
characterization for federal income tax purposes. Also, due to the timing of
dividend distributions, the fiscal year in which amounts are distributed may
differ from the year that the income or realized gains (losses) were recorded by
the Fund.

Dividends to shareholders

An annual dividend from net investment income, declared and paid at the end of
the calendar year, when available, is reinvested in additional shares of the
Fund at net asset value or payable in cash. Capital gains, when available, are
distributed along with the income dividend.

- --------------------------------------------------------------------------------
27   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


2. EXPENSES AND SALES CHARGES

In addition to the expenses allocated from the Portfolio, the Fund accrues its
own expenses as follows:

The Fund has an agreement with AEFC to provide administrative services. Under an
Administrative Services Agreement, the Fund pays AEFC a fee for administration
and accounting services at a percentage of the Fund's average daily net that
declines from 0.05% to 0.02% annually as the Fund's assets increase. A minor
portion of additional administrative service expenses paid by the Fund are
consultants' fees and fund office expenses. Under this agreement, the Fund also
pays taxes, audit and certain legal fees, registration fees for shares,
compensation of board members, corporate filing fees and any other expenses
properly payable by the Fund and approved by the board.

Under a Deferred Compensation Plan (the Plan), non-interested board members may
defer receipt of their compensation. Deferred amounts are treated as though
equivalent dollar amounts had been invested in shares of the Fund or other
American Express mutual funds. The Fund's liability for these amounts is
adjusted for market value changes and remains in the Fund until distributed in
accordance with the Plan.

Under a separate Transfer Agency Agreement, American Express Client Service
Corporation (AECSC) maintains shareholder accounts and records. The Fund pays
AECSC an annual fee per shareholder account for this service as follows:

o  Class A $19.50

o  Class B $20.50

o  Class C $20.00

o  Class Y $17.50

The incremental transfer agency fee is the amount charged to the specific
classes for the additional expense above the fee for Class Y.

Class I pays a transfer agency fee at an annual rate per shareholder account of
$1. This amount is included in the transfer agency fee on the statement of
operations.

In addition, AECSC is entitled to charge an annual closed account fee of $5 per
inactive account, charged on a pro rata basis from the date the account becomes
inactive until the date the account is purged from the transfer agent system
generally within one year. However, the closed account fee is currently not
effective.

The Fund has agreements with American Express Financial Advisors Inc. (the
Distributor) for distribution and shareholder services. Under a Plan and
Agreement of Distribution pursuant to Rule 12b-1, the Fund pays a fee at an
annual rate up to 0.25% of the Fund's average daily net assets attributable to
Class A shares and up to 1.00% for Class B and Class C shares.

Under a Shareholder Service Agreement, the Fund pays the Distributor a fee for
service provided to shareholders by financial advisors and other servicing
agents. The fee is calculated at a rate of 0.10% of the Fund's average daily net
assets attributable to Class Y shares.

- --------------------------------------------------------------------------------
28   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Sales charges received by the Distributor for distributing Fund shares were
$4,820,787 for Class A, $1,988,359 for Class B and $5,708 for Class C for the
six months ended Jan. 31, 2005.

During the six months ended Jan. 31, 2005, the Fund's transfer agency fees were
reduced by $157,139 as a result of earnings credits from overnight cash
balances.

3. CAPITAL SHARE TRANSACTIONS

Transactions in shares of capital stock for the periods indicated are as
follows:



                                                              Six months ended Jan. 31, 2005
                                              Class A         Class B      Class C      Class I        Class Y
                                                                                    
Sold                                        7,704,852       3,468,562      187,844    1,712,246      6,466,417
Issued for reinvested distributions         5,161,745         941,876       20,960       28,563      1,945,491
Redeemed                                  (64,999,046)    (22,390,133)    (567,105)      (5,203)   (23,529,134)
                                          -----------     -----------     --------       ------    -----------
Net increase (decrease)                   (52,132,449)    (17,979,695)    (358,301)   1,735,606    (15,117,226)
                                          -----------     -----------     --------    ---------    -----------

                                                                 Year ended July 31, 2004
                                              Class A         Class B      Class C     Class I*        Class Y
Sold                                       41,994,227      13,241,759      694,168      797,528     27,893,281
Fund merger                                 6,143,014       3,220,859      223,688           --          1,053
Issued for reinvested distributions         1,922,552              --           --        1,014        922,930
Redeemed                                  (87,457,046)    (49,430,022)    (773,898)        (462)   (51,317,577)
                                          -----------     -----------     --------         ----    -----------
Net increase (decrease)                   (37,397,253)    (32,967,404)     143,958      798,080    (22,500,313)
                                          -----------     -----------      -------      -------    -----------


* Inception date was March 4, 2004.

4. BANK BORROWINGS

The Fund has a revolving credit agreement with a syndicate of banks headed by
The Bank of New York, whereby the Fund may borrow for the temporary funding of
shareholder redemptions or for other temporary or emergency purposes. The
agreement went into effect Sept. 21, 2004. The Fund must maintain asset coverage
for borrowings of at least 300%. The agreement, which enables the Fund to
participate with other American Express mutual funds, permits borrowings up to
$500 million, collectively. Interest is charged to each Fund based on its
borrowings at a rate equal to either the higher of the Federal Funds Effective
Rate plus 0.50% or the Prime Lending Rate. Borrowings are payable within 60 days
after such loan is executed. The Fund also pays a commitment fee equal to its
pro rata share of the amount of the credit facility at a rate of 0.09% per
annum. Prior to this agreement, the Fund had a revolving credit agreement that
permitted borrowings up to $500 million with Deutsche Bank. The Fund had no
borrowings outstanding during the six months ended Jan. 31, 2005.

- --------------------------------------------------------------------------------
29   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


5. CAPITAL LOSS CARRY-OVER

For federal income tax purposes, the Fund had a capital loss carry-over of
$67,590,843 that if not offset by future capital gains realized after July 31,
2004 will expire as follows:

                2007         2008         2009          2010         2011
             $651,698    $7,174,242   $47,082,209  $8,294,019   $4,388,675

AXP New Dimensions Fund acquired $80,136,732 of capital loss carry-overs in
connection with the AXP Growth Dimensions Fund and AXP Focused Growth Fund
merger (Note 6). In addition to the acquired capital loss carry-overs, the Fund
also acquired unrealized capital gains as a result of the mergers. The yearly
utilization of the acquired capital losses as well as the utilization of the
acquired unrealized losses is limited by the Internal Revenue Code. It is
unlikely the board will authorize a distribution of any net realized capital
gains until the available capital loss carry-over has been offset or expires.

6. FUND MERGER

At the close of business on June 25, 2004, AXP New Dimensions Fund acquired the
assets and assumed the identified liabilities of AXP Focused Growth Fund and AXP
Growth Dimensions Fund. Upon receipt of the investments and related assets and
liabilities from AXP Focused Growth Fund and AXP Growth Dimensions Fund, AXP New
Dimensions Fund made an in-kind contribution of $211,872,382 to Growth Trends
Portfolio. This reorganization was completed after shareholders approved the
plan on June 9, 2004.

The aggregate net assets of AXP New Dimensions Fund immediately before the
acquisition was $16,149,643,433 and the combined net assets immediately after
the acquisition was $16,371,515,815.

The merger was accomplished by a tax-free exchange of the following:

                                             Shares            Value
AXP Focused Growth Fund                    23,415,522      $ 42,348,160
AXP Growth Dimensions Fund                 74,295,087       179,524,222

In exchange for the AXP Focused Growth Fund and AXP Growth Dimensions Fund
shares and net assets, AXP New Dimensions Fund issued the following number of
shares:

                                                               Shares
Class A                                                       6,143,014
Class B                                                       3,220,859
Class C                                                         223,688
Class Y                                                           1,053

AXP Focused Growth Fund's and AXP Growth Dimensions Fund's net assets after
adjustments for any permanent book-to-tax differences at the merger date were as
follows, which include the following amounts of capital stock, unrealized
appreciation, accumulated net realized loss and temporary book-to-tax
differences.



                                                                                      Accumulated         Temporary
                                   Total net        Capital          Unrealized            net            book-to-tax
                                    assets            stock         appreciation      realized loss       differences
                                                                                           
AXP Focused Growth Fund         $ 42,348,160      $ 47,925,406       $ 5,187,878     $(10,453,291)        $(311,833)
AXP Growth Dimensions Fund       179,524,222       234,495,050        18,406,183      (72,853,762)         (523,249)


- --------------------------------------------------------------------------------
30   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


7. FINANCIAL HIGHLIGHTS

The tables below show certain important financial information for evaluating the
Fund's results.



Class A
Per share income and capital changes(a)
Fiscal period ended July 31,                                               2005(f)       2004         2003         2002       2001
                                                                                                            
Net asset value, beginning of period                                     $22.58        $21.90       $20.04       $25.43     $36.26
                                                                         ------        ------       ------       ------     ------
Income from investment operations:
Net investment income (loss)                                                .14           .08          .07          .05        .02
Net gains (losses) (both realized and unrealized)                          1.01           .71         1.82        (5.42)     (7.37)
                                                                         ------        ------       ------       ------     ------
Total from investment operations                                           1.15           .79         1.89        (5.37)     (7.35)
                                                                         ------        ------       ------       ------     ------
Less distributions:
Dividends from net investment income                                       (.16)         (.11)        (.03)        (.02)      (.01)
Excess distributions from net investment income                              --            --           --           --       (.01)
Distributions from realized gains                                          (.18)           --           --           --      (3.46)
                                                                         ------        ------       ------       ------     ------
Total distributions                                                        (.34)         (.11)        (.03)        (.02)     (3.48)
                                                                         ------        ------       ------       ------     ------
Net asset value, end of period                                           $23.39        $22.58       $21.90       $20.04     $25.43
                                                                         ------        ------       ------       ------     ------
Ratios/supplemental data
Net assets, end of period (in millions)                                  $8,433        $9,319       $9,859       $9,863    $13,857
Ratio of expenses to average daily net assets(b)                           .96%(c)       .91%        1.08%        1.06%      1.00%
Ratio of net investment income (loss) to average daily net assets         1.12%(c)       .45%         .42%         .19%       .12%
Portfolio turnover rate (excluding short-term securities)                   32%           49%          20%          27%        29%
Total return(d)                                                           5.07%(e)      3.59%        9.47%      (21.14%)   (21.10%)


(a)  For a share outstanding throughout the period. Rounded to the nearest cent.

(b)  Expense ratio is based on total expenses of the Fund before reduction of
     earnings credits on cash balances.

(c)  Adjusted to an annual basis.

(d)  Total return does not reflect payment of a sales charge.

(e)  Not annualized.

(f)  Six months ended Jan. 31, 2005 (Unaudited).

- --------------------------------------------------------------------------------
31   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Class B
Per share income and capital changes(a)
Fiscal period ended July 31,                                              2005(f)       2004         2003         2002       2001
                                                                                                            
Net asset value, beginning of period                                     $21.34        $20.77       $19.12       $24.44     $35.22
                                                                         ------        ------       ------       ------     ------
Income from investment operations:
Net investment income (loss)                                                .01          (.10)        (.04)        (.14)      (.13)
Net gains (losses) (both realized and unrealized)                           .99           .67         1.69        (5.16)     (7.19)
                                                                         ------        ------       ------       ------     ------
Total from investment operations                                           1.00           .57         1.65        (5.30)     (7.32)
                                                                         ------        ------       ------       ------     ------
Less distributions:
Dividends from net investment income                                         --            --           --         (.02)        --
Distributions from realized gains                                          (.18)           --           --           --      (3.46)
                                                                         ------        ------       ------       ------     ------
Total distributions                                                        (.18)           --           --         (.02)     (3.46)
                                                                         ------        ------       ------       ------     ------
Net asset value, end of period                                           $22.16        $21.34       $20.77       $19.12     $24.44
                                                                         ------        ------       ------       ------     ------
Ratios/supplemental data
Net assets, end of period (in millions)                                  $2,560        $2,849       $3,457       $3,728     $5,169
Ratio of expenses to average daily net assets(b)                          1.73%(c)      1.68%        1.85%        1.83%      1.76%
Ratio of net investment income (loss) to average daily net assets          .35%(c)      (.32%)       (.35%)       (.57%)     (.65%)
Portfolio turnover rate (excluding short-term securities)                   32%           49%          20%          27%        29%
Total return(d)                                                            .67%(e)      2.74%        8.63%      (21.71%)   (21.69%)


(a)  For a share outstanding throughout the period. Rounded to the nearest cent.

(b)  Expense ratio is based on total expenses of the Fund before reduction of
     earnings credits on cash balances.

(c)  Adjusted to an annual basis.

(d)  Total return does not reflect payment of a sales charge.

(e)  Not annualized.

(f)  Six months ended Jan. 31, 2005 (Unaudited).

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32   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Class C
Per share income and capital changes(a)
Fiscal period ended July 31,                                               2005(f)       2004         2003         2002       2001
                                                                                                            
Net asset value, beginning of period                                     $21.32        $20.74       $19.10       $24.42     $35.23
                                                                         ------        ------       ------       ------     ------
Income from investment operations:
Net investment income (loss)                                                .01          (.09)        (.04)        (.14)      (.13)
Net gains (losses) (both realized and unrealized)                           .98           .67         1.68        (5.16)     (7.19)
                                                                         ------        ------       ------       ------     ------
Total from investment operations                                            .99           .58         1.64        (5.30)     (7.32)
                                                                         ------        ------       ------       ------     ------
Less distributions:
Dividends from net investment income                                         --            --           --         (.02)      (.02)
Excess distributions from net investment income                              --            --           --           --       (.01)
Distributions from realized gains                                          (.18)           --           --           --      (3.46)
                                                                         ------        ------       ------       ------     ------
Total distributions                                                        (.18)           --           --         (.02)     (3.49)
                                                                         ------        ------       ------       ------     ------
Net asset value, end of period                                           $22.13        $21.32       $20.74       $19.10     $24.42
                                                                         ------        ------       ------       ------     ------
Ratios/supplemental data
Net assets, end of period (in millions)                                     $58           $63          $59          $44        $30
Ratio of expenses to average daily net assets(b)                          1.74%(c)      1.69%        1.87%        1.85%      1.76%
Ratio of net investment income (loss) to average daily net assets          .34%(c)      (.33%)       (.38%)       (.60%)     (.75%)
Portfolio turnover rate (excluding short-term securities)                   32%           49%          20%          27%        29%
Total return(d)                                                           4.62%(e)      2.80%        8.59%      (21.73%)   (21.70%)


(a)  For a share outstanding throughout the period. Rounded to the nearest cent.

(b)  Expense ratio is based on total expenses of the Fund before reduction of
     earnings credits on cash balances.

(c)  Adjusted to an annual basis.

(d)  Total return does not reflect payment of a sales charge.

(e)  Not annualized.

(f)  Six months ended Jan. 31, 2005 (Unaudited).

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33   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Class I
Per share income and capital changes(a)
Fiscal period ended July 31,                                              2005(g)       2004(b)
                                                                                 
Net asset value, beginning of period                                     $22.71        $24.37
                                                                         ------        ------
Income from investment operations:
Net investment income (loss)                                                .24           .06
Net gains (losses) (both realized and unrealized)                           .97         (1.67)
                                                                         ------        ------
Total from investment operations                                           1.21         (1.61)
                                                                         ------        ------
Less distributions:
Dividends from net investment income                                       (.26)         (.05)
Distributions from realized gains                                          (.18)           --
                                                                         ------        ------
Total distributions                                                        (.44)           --
                                                                         ------        ------
Net asset value, end of period                                           $23.48        $22.71
                                                                         ------        ------
Ratios/supplemental data
Net assets, end of period (in millions)                                     $59           $18
Ratio of expenses to average daily net assets(c)                           .55%(d)       .50%(d)
Ratio of net investment income (loss) to average daily net assets        .1.43%(d)     .87%(d)
Portfolio turnover rate (excluding short-term securities)                   32%           49%
Total return(e)                                                           5.28%(f)     (6.61%)(f)


(a)  For a share outstanding throughout the period. Rounded to the nearest cent.

(b)  Inception date was March 4, 2004.

(c)  Expense ratio is based on total expenses of the Fund before reduction of
     earnings credits on cash balances.

(d)  Adjusted to an annual basis.

(e)  Total return does not reflect payment of a sales charge.

(f)  Not annualized.

(g)  Six months ended Jan. 31, 2005 (Unaudited).

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34   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




Class Y
Per share income and capital changes(a)
Fiscal period ended July 31,                                              2005(f)       2004         2003         2002       2001
                                                                                                            
Net asset value, beginning of period                                     $22.70        $22.02       $20.14       $25.51     $36.33
                                                                         ------        ------       ------       ------     ------
Income from investment operations:
Net investment income (loss)                                                .18           .11          .11          .09        .07
Net gains (losses) (both realized and unrealized)                          1.00           .72         1.83        (5.44)     (7.38)
                                                                         ------        ------       ------       ------     ------
Total from investment operations                                           1.18           .83         1.94        (5.35)     (7.31)
                                                                         ------        ------       ------       ------     ------
Less distributions:
Dividends from net investment income                                       (.20)         (.15)        (.06)        (.02)      (.02)
Excess distributions from net investment income                              --            --           --           --       (.03)
Distributions from realized gains                                          (.18)           --           --           --      (3.46)
                                                                         ------        ------       ------       ------     ------
Total distributions                                                        (.38)         (.15)        (.06)        (.02)     (3.51)
                                                                         ------        ------       ------       ------     ------
Net asset value, end of period                                           $23.50        $22.70       $22.02       $20.14     $25.51
                                                                         ------        ------       ------       ------     ------
Ratios/supplemental data
Net assets, end of period (in millions)                                  $2,821        $3,068       $3,472       $3,222     $4,677
Ratio of expenses to average daily net assets(b)                           .79%(c)       .75%         .91%         .90%       .84%
Ratio of net investment income (loss) to average daily net assets         1.28%(c)       .61%         .59%         .36%       .28%
Portfolio turnover rate (excluding short-term securities)                   32%           49%          20%          27%        29%
Total return(d)                                                           5.18%(e)      3.75%        9.64%      (21.00%)   (20.97%)


(a)  For a share outstanding throughout the period. Rounded to the nearest cent.

(b)  Expense ratio is based on total expenses of the Fund before reduction of
     earnings credits on cash balances.

(c)  Adjusted to an annual basis.

(d)  Total return does not reflect payment of a sales charge.

(e)  Not annualized.

(f)  Six months ended Jan. 31, 2005 (Unaudited).

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35   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Fund Expenses Example

(UNAUDITED)

As a shareholder of the Fund, you incur two types of costs: (1) transaction
costs, including sales charges (loads) on purchase payments; and (2) ongoing
costs, including management fees; distribution and service (12b-1) fees; and
other Fund expenses. This example is intended to help you understand your
ongoing costs (in dollars) of investing in the Fund and to compare these costs
with the ongoing costs of investing in other mutual funds.

The example is based on an investment of $1,000 invested at the beginning of the
period and held for the six months ended Jan. 31, 2005.

Actual Expenses

The first line of the table provides information about actual account values and
actual expenses. You may use the information in this line, together with the
amount you invested, to estimate the expenses that you paid over the period.
Simply divide your account value by $1,000 (for example, an $8,600 account value
divided by $1,000 = 8.6), then multiply the result by the number in the first
line under the heading titled "Expenses paid during the period" to estimate the
expenses you paid on your account during this period.

Hypothetical Example for Comparison Purposes

The second line of the table provides information about hypothetical account
values and hypothetical expenses based on the Fund's actual expense ratio and an
assumed rate of return of 5% per year before expenses, which is not the Fund's
actual return. The hypothetical account values and expenses may not be used to
estimate the actual ending account balance or expenses you paid for the period.
You may use this information to compare the ongoing costs of investing in the
Fund and other funds. To do so, compare this 5% hypothetical example with the 5%
hypothetical examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your
ongoing costs only and do not reflect any transactional costs, such as sales
charges (loads). Therefore, the second line of the table is useful in comparing
ongoing costs only, and will not help you determine the relative total costs of
owning different funds. In addition, if these transactional costs were included,
your costs would have been higher.

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36   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT




                                                      Beginning            Ending             Expenses
                                                     account value      account value       paid during        Annualized
                                                     Aug. 1, 2004       Jan. 31, 2005       the period(a)     expense ratio
Class A
                                                                                                      
     Actual(b)                                          $1,000            $1,050.70            $4.99              0.96%
     Hypothetical (5% return before expenses)           $1,000            $1,020.48            $4.92              0.96%
Class B
     Actual(b)                                          $1,000            $1,046.70            $8.97              1.73%
     Hypothetical (5% return before expenses)           $1,000            $1,016.57            $8.84              1.73%
Class C
     Actual(b)                                          $1,000            $1,046.20            $9.02              1.74%
     Hypothetical (5% return before expenses)           $1,000            $1,016.52            $8.89              1.74%
Class I
     Actual(b)                                          $1,000            $1,052.80            $2.86              0.55%
     Hypothetical (5% return before expenses)           $1,000            $1,022.55            $2.82              0.55%
Class Y
     Actual(b)                                          $1,000            $1,051.80            $4.11              0.79%
     Hypothetical (5% return before expenses)           $1,000            $1,021.34            $4.05              0.79%


(a)  Expenses are equal to the Fund's annualized expense ratio as indicated
     above, multiplied by the average account value over the period, multiplied
     by 185/365 (to reflect the one-half year period).

(b)  Based on the actual return for the six months ended Jan. 31, 2005: +5.07%
     for Class A, +4.67% for Class B, +4.62% for Class C, +5.28% for Class I and
     +5.18% for Class Y.

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37   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


Proxy Voting

The policy of the Board is to vote all proxies of the companies in which the
Fund holds investments. The procedures are stated in the Statement of Additional
Information (SAI). You may obtain a copy of the SAI without charge by calling
(800) 862-7919; by looking at the website americanexpress.com/funds; or by
searching the website of the Securities and Exchange Commission
http://www.sec.gov. You may view the Fund's voting record for all portfolio
companies whose shareholders meetings were completed the previous quarter on
americanexpress.com/funds or obtain a copy by calling the Fund's administrator,
Board Services Corporation, collect at (612) 330-9283. In addition, information
regarding how the Fund voted proxies relating to portfolio securities during the
most recent 12-month period ended June 30 is available at http://www.sec.gov.

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38   ---   AXP NEW DIMENSIONS FUND   ---   2005 SEMIANNUAL REPORT


(logo)
AMERICAN
 EXPRESS
(R)


American Express Funds
70100 AXP Financial Center
Minneapolis, MN 55474

This report must be accompanied or preceded by the Fund's current prospectus.
Distributed by American Express Financial Advisors Inc. Member NASD. American
Express Company is separate from American Express Financial Advisors Inc. and is
not a broker-dealer.


Item 2.    Code of Ethics. Not applicable for semi-annual reports.

Item 3.    Audit Committee Financial Expert. Not applicable for semi-annual
           reports.

Item 4.    Principal Accountant Fees and Services.  Not applicable for
           semi-annual reports.

Item 5.    Audit Committee of Listed Registrants. Not applicable.

Item 6.    The complete schedule of investments is included in Item 1 of this
           Form N-CSR.

Item 7.    Disclosure of Proxy Voting Policies and Procedures for Closed-End
           Management Investment Companies. Not applicable.

Item 8.    Portfolio Managers of Closed-End Management Investment Companies.
           Not applicable.

Item 9.    Purchase of Equity Securities by Closed-End Management Investment
           Company and Affiliated Purchasers. Not applicable.

Item 10.   Submission of matters to a vote of security holders. Not applicable.

Item 11.   Controls and Procedures.

           (a) Based upon their evaluation of the registrant's disclosure
           controls and procedures as conducted within 90 days of the filing
           date of this Form N-CSR, the registrant's Principal Financial
           Officer and Principal Executive Officer have concluded that those
           disclosure controls and procedures provide reasonable assurance
           that the material information required to be disclosed by the
           registrant on this report is recorded, processed, summarized and
           reported within the time periods specified in the Securities and
           Exchange Commission's rules and forms.

           (b) There were no changes in the registrant's internal controls over
           financial reporting that occurred during the registrant's last fiscal
           half-year (the registrant's second fiscal half-year in the case of an
           annual report) that has materially affected, or is reasonably likely
           to materially affect, the registrant's internal control over
           financial reporting.

Item 12.   Exhibits.

           (a)(1) Not applicable for semi-annual reports.

           (a)(2) Separate  certification  for the  Registrant's  principal
           executive officer and principal financial officer, as required by
           Section 302 of the  Sarbanes-Oxley  Act of 2002 and Rule 30a-2(a)
           under  the  Investment  Company  Act of  1940,  are  attached  as
           EX.99.CERT.

           (a)(3) Not applicable.

           (b) A certification by the Registrant's  principal executive officer
           and principal financial officer, pursuant to Section 906 of the
           Sarbanes-Oxley Act of 2002 and Rule 30a-2(b) under the Investment
           Company Act of 1940, is attached as EX.99.906 CERT.


                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)                  AXP Dimensions Series, Inc.


By                        /s/ Paula R. Meyer
                          ------------------
                              Paula R. Meyer
                              President and Principal Executive Officer

Date                          March 30, 2005

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment  Company  Act of  1940,  this  report  has been  signed  below by the
following  persons on behalf of the  registrant and in the capacities and on the
dates indicated.


By                        /s/ Paula R. Meyer
                          ------------------
                              Paula R. Meyer
                              President and Principal Executive Officer

Date                          March 30, 2005


By                        /s/ Jeffrey P. Fox
                          ------------------
                              Jeffrey P. Fox
                              Treasurer and Principal Financial Officer

Date                          March 30, 2005