Item 1. Report to Shareholders

T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
June 30, 2004

Certified Semiannual Report

This report is certified under the Sarbanes-Oxley Act of 2002, which requires
that public companies, including mutual funds, affirm that the information
provided in their annual and semiannual shareholder reports fully and fairly
represents their financial position.



T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)

FINANCIAL HIGHLIGHTS             For a share outstanding throughout each period
- --------------------------------------------------------------------------------

                 6 Months       Year
                    Ended      Ended
                  6/30/04   12/31/03  12/31/02   12/31/01   12/31/00   12/31/99
NET ASSET VALUE

Beginning of
period           $  24.80  $   16.61  $  22.63  $   23.89  $   27.53  $   23.34

Investment
activities

  Net investment
  income (loss)     (0.09)     (0.15)    (0.17)     (0.17)     (0.13)     (0.15)

  Net realized
  and unrealized
  gain (loss)        1.91       8.34     (5.85)     (0.53)     (0.37)      7.36

  Total from
  investment
  activities         1.82       8.19     (6.02)     (0.70)     (0.50)      7.21

Distributions

  Net realized
  gain                  -          -         -      (0.56)     (3.14)     (3.02)

NET ASSET VALUE

End of period    $  26.62  $   24.80  $  16.61  $   22.63  $   23.89  $   27.53
                 --------------------------------------------------------------

Ratios/Supplemental
Data

Total return^       7.34%     49.31%  (26.60)%    (2.84)%    (1.86)%     32.52%

Ratio of total
expenses to
average net
assets              0.87%!     0.91%     0.92%      0.91%      0.88%      0.90%

Ratio of net
investment
income (loss)
to average
net assets        (0.69)%!   (0.75)%   (0.81)%    (0.77)%    (0.51)%    (0.66)%

Portfolio
turnover rate       28.9%!     28.6%     23.7%      27.4%      47.2%      44.7%

Net assets,
end of period
(in millions)    $  5,371  $   4,955  $  3,359  $   5,583  $   6,122  $   6,022

   ^ Total return reflects the rate that an investor would have earned on an
     investment in the fund during each period, assuming reinvestment of all
     distributions.

   ! Annualized

The accompanying notes are an integral part of these financial statements.



T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)                           June 30, 2004

PORTFOLIO OF INVESTMENTS (1)                            Shares            Value
- --------------------------------------------------------------------------------
(Cost and value in $ 000s)

EQUITY INVESTMENTS 99.6% (s.)

CONSUMER DISCRETIONARY   20.1%

Auto Components   0.1%

LKQ Corporation *                                      192,900            3,575

                                                                          3,575


Hotels, Restaurants & Leisure   5.9%

CEC Entertainment *                                    750,000           22,133

Life Time Fitness *                                    445,000            9,345

Multimedia Games *!                                  2,000,000           53,640

Panera Bread, Class A *                              1,000,000           35,880

PF Chang's China Bistro *                            1,000,000           41,150

Rare Hospitality International *                     1,125,000           28,012

Ruby Tuesday                                         1,000,000           27,450

Sonic *                                              1,096,892           24,954

Station Casinos                                      1,175,000           56,870

WMS Industries *                                       487,100           14,516

                                                                        313,950


Household Durables   2.7%

Ryland Group                                           500,000           39,100

Toll Brothers *                                      1,800,000           76,176

WCI Communities *                                      240,000            5,354

Yankee Candle Company *                                800,000           23,400

                                                                        144,030


Internet & Catalog Retail   0.2%

priceline.com *                                        500,000           13,465

                                                                         13,465


Media   4.4%

ADVO                                                 1,250,000           41,150

Catalina Marketing *                                 2,132,500           39,003

Cox Radio, Class A *                                 1,000,000           17,380

Entercom Communications *                            1,000,000           37,300

Radio One, Class D *                                 2,123,778           34,002

Regent Communications *                              1,700,200           10,524

Spanish Broadcasting, Class A *!                     2,500,000           23,275

TiVo *                                                 800,000            5,672




Westwood One *                                         150,000            3,570

XM Satellite Radio Holdings, Class A *               1,000,000           27,290

                                                                        239,166


Multiline Retail   1.2%

Tuesday Morning *!                                   2,231,900           64,725

                                                                         64,725


Specialty Retail   5.6%

AC Moore Arts & Crafts *                               857,800           23,598

AnnTaylor Stores *                                   1,500,000           43,470

Christopher & Banks !                                2,000,000           35,420

Guitar Center *                                         83,100            3,695

Hot Topic *                                            250,000            5,123

Linens 'n Things *                                     600,000           17,586

O'Reilly Automotive *                                1,800,000           81,360

PETCO Animal Supplies *                              1,200,000           38,652

Sonic Automotive, Class A                              750,000           16,613

The Finish Line, Class A *                             850,000           25,645

Tweeter Home Entertainment Group *                     863,043            4,660

Ultimate Electronics *!                                800,000            3,952

                                                                        299,774

Total Consumer Discretionary                                          1,078,685


CONSUMER STAPLES   0.3%

Food & Staples Retailing   0.3%

Duane Reade *                                        1,000,000           16,330

Total Consumer Staples                                                   16,330


ENERGY   5.2%

Energy Equipment & Services   4.6%

BJ Services *                                          350,000           16,044

Cooper Cameron *                                       300,000           14,610




FMC Technologies *                                   1,500,000           43,200

Grant Prideco *                                      1,522,100           28,098

Helmerich & Payne                                      900,000           23,535

Hydril *                                               531,000           16,727

Key Energy Services *                                1,500,000           14,160

National Oilwell *                                     950,000           29,915

Smith International *                                  250,000           13,940

Tidewater                                              700,000           20,860

Varco International *                                  400,000            8,756

W-H Energy Services *                                  784,000           15,366

                                                                        245,211


Oil & Gas   0.6%

Cimarex Energy *                                       550,000           16,627

Encore Aquisition *                                    620,000           17,298

                                                                         33,925

Total Energy                                                            279,136


FINANCIALS   8.2%

Capital Markets   2.5%

Affiliated Managers Group *                            531,000           26,746

Greenhill *                                            135,500            2,833

Investor's Financial Services                          800,000           34,864

Legg Mason                                             350,000           31,854

National Financial Partners                            500,000           17,635

Waddell & Reed Financial, Class A                    1,050,000           23,216

                                                                        137,148


Commercial Banks   1.4%

Boston Private Financial                               350,000            8,106

Signature Bank *                                        83,400            1,981

Silicon Valley Bancshares *                            266,000           10,547




Texas Capital Bancshares *                             600,000            9,960

UCBH Holdings                                        1,200,000           47,424

                                                                         78,018


Consumer Finance   0.6%

First Marblehead *                                     450,000           18,117

Moneygram International *                              250,000            5,150

Nelnet, Class A *                                      400,000            7,100

                                                                         30,367


Diversified Financial Services   0.8%

Assured Guaranty *                                     560,000            9,492

CapitalSource *                                      1,350,000           33,008

                                                                         42,500


Insurance   2.0%

Direct General                                         526,100           16,972

Hilb Rogal and Hamilton                                209,600            7,479

Hub International                                      400,000            7,636

Infinity Property & Casualty                           625,000           20,625

MaxRe Capital                                          700,000           13,636

Platinum Underwriters                                  550,000           16,736

Scottish Annuity & Life                              1,000,000           23,250

                                                                        106,334


Thrifts & Mortgage Finance   0.9%

Radian Group                                         1,000,000           47,900

                                                                         47,900

Total Financials                                                        442,267


HEALTH CARE   21.1%

Biotechnology   7.1%

Abgenix *                                              875,000           10,255

Acadia Pharmaceuticals *                               700,000            4,340

Alexion Pharmaceutical *                               500,000            9,300

Alkermes *                                           1,681,700           22,871

Amylin Pharmaceuticals *                               550,000           12,540




Anadys Pharmaceuticals *                               607,100            4,310

Angiotech Pharmaceuticals *                            127,700            2,573

BioCryst Pharmaceuticals *                             323,400            2,231

Cephalon *                                             699,500           37,773

Cubist Pharmaceuticals *                             1,025,000           11,377

Cytogen *                                              400,000            6,360

Cytokinetics *                                          62,500              928

deCODE GENETICS *                                    1,550,000           13,175

Diversa *                                            1,400,000           14,182

Dynavax Technologies *                                 360,000            2,398

EXACT Sciences *                                       400,000            2,460

Exelixis *                                           1,350,000           13,621

Eyetech Pharmaceuticals *                              125,000            5,365

Gilead Sciences *                                       25,000            1,675

Human Genome Sciences *                                450,000            5,234

ImClone Systems *                                      150,000           12,868

Keryx Biopharmaceuticals *                             275,000            3,482

Kosan Biosciences *                                    209,600            1,656

Lexicon Genetics *                                   1,000,000            7,840

Memory Pharmaceuticals *                               500,000            4,551

Momenta Pharmaceuticals *                              650,000            5,850

Myogen *                                               150,000            1,164

Myriad Genetics *                                    1,000,000           14,920

Neurocrine Biosciences *                               960,500           49,802

NPS  Pharmaceuticals *                               1,210,000           25,410

ONYX Pharmaceuticals *                                 500,000           21,180

Protein Design Labs *                                  175,000            3,348

Rigel Pharmaceuticals *                                393,900            5,597

Senomyx *                                              870,000            5,438

Theravance, Pfd., Series D1 *!!@                       513,334            4,620

Transkaryotic Therapies *                              400,000            5,984

Trimeris *                                             519,400            7,495

United Therapeutics *                                  175,000            4,489

Vertex Pharmaceuticals *                               675,000            7,317

Vicuron Pharmaceuticals *                              100,000            1,256




Vion Pharmaceuticals *                                 250,000            1,040

ViroPharma *                                           509,000              911

XOMA *                                                 425,000            1,904

                                                                        381,090

Health Care Equipment & Supplies   1.4%

Advanced Neuromodulation Systems *                     150,000            4,920

Analogic                                               120,000            5,092

Control Delivery Systems, Cvt. Pfd.,
8.00%, Series A *!!@                                    74,432            2,000

CTI Molecular Imaging *                                350,000            4,963

Encore Medical *                                       446,265            2,812

Endologix *                                            682,500            3,337

EPIX Medical *                                         450,000            9,495

Integra LifeServices Holdings *                        544,100           19,190

Nuvasive *                                             155,000            1,691

Regeneration Technologies *                            200,000            2,146

Thoratec *                                             700,000            7,511

Wilson Greatbatch Technologies *                       400,000           11,180

                                                                         74,337


Health Care Providers & Services   10.6%

Accredo Health *                                       350,000           13,633

Advisory Board *                                       300,000           10,680

Community Health System *                            1,000,000           26,770

Coventry Health Care *                               1,275,000           62,347

Davita *                                             3,400,000          104,822

HealthStream *!                                      2,405,000            4,764

Henry Schein *                                       2,100,000          132,594

LabOne *                                               300,000            9,534

Mariner Health Care *                                  555,600           14,960

Omnicare                                             3,000,000          128,430

Symbion *                                              143,300            2,502

United Surgical Partners International *               350,000           13,814

VCA Antech *                                           800,000           35,856

WellChoice *                                           300,000           12,420

                                                                        573,126




Pharmaceuticals   2.0%

Able Laboratories *                                    544,800           11,201

Atherogenics *                                         850,000           16,175

Inspire Phamaceuticals *                             1,000,000           16,720

Medicines Company *                                    753,900           23,001

MGI Pharma *                                           200,000            5,402

Nektar Therapeutics *                                  300,000            5,988

Noven Pharmaceuticals *                                375,000            8,258

Salix Pharmaceuticals *                                300,000            9,885

Taro Pharmaceuticals, Class A *                        233,300           10,149

                                                                        106,779

Total Health Care                                                     1,135,332



INDUSTRIALS & BUSINESS SERVICES   17.8%

Aerospace & Defense   1.5%

Armor Holdings *                                       775,000           26,350

Mercury Computer Systems *                             600,000           14,880

MTC Technologies *                                     200,000            5,164

Triumph Group *                                        600,000           19,158

United Defense Industries *                            435,000           15,225

                                                                         80,777


Air Freight & Logistics   0.3%

EGL *                                                  300,000            7,980

Forward Air *                                          200,000            7,480

                                                                         15,460


Commercial Services & Supplies   12.5%

Apollo Group, Class A *                              2,150,000          189,823

Bright Horizons Family Solutions *                     400,000           21,444

Corporate Executive Board                              798,800           46,163

Education Management *                               1,300,000           42,718

Exult *                                              4,750,000           25,555

First Advantage, Class A *                             241,400            4,562

Intersections *                                         78,000            1,871

Laureate *                                           1,650,000           63,096

LECG *                                                 500,000            8,655




Mobile Mini *!                                       1,100,000           31,251

Resources Connection *                                 498,000           19,477

School Specialty *!                                  1,500,000           54,465

SOURCECORP *                                           500,000           13,760

Tetra Tech *                                           900,000           14,688

University of Phoenix Online *                       1,000,000           87,590

Waste Connections *                                  1,500,100           44,493

                                                                        669,611


Industrial Conglomerates   1.0%

Roper Industries                                       950,000           54,055

                                                                         54,055


Machinery   2.1%

Actuant Corporation, Class A *                       1,168,700           45,568

Oshkosh Truck                                        1,200,000           68,772

                                                                        114,340


Trading Companies & Distributors   0.4%

MSC Industrial Direct                                  650,000           21,346

                                                                         21,346

Total Industrials & Business Services                                   955,589


INFORMATION TECHNOLOGY   21.5%

Communications Equipment   1.7%

Black Box                                              200,000            9,452

Bookham Technology ADR *                             3,000,000            2,880

Emulex *                                             1,550,000           22,180

F5 Networks *                                          750,000           19,860

Harmonic *                                             800,000            6,816

Packeteer *                                            700,500           11,313

Sirf Technology Holdings *                             550,000            7,189

Tekelec *                                              500,000            9,085

                                                                         88,775


Computers & Peripherals   0.0%

Synaptics *                                            100,000            1,915

                                                                          1,915


Electronic Equipment & Instruments   1.2%

Daktronics *                                           100,000            2,495

Digital Theater Systems *                              500,000           13,075

Molex                                                  100,000            3,208

National Instruments                                   500,000           15,325

Newport *                                              925,000           14,957

Trimble Navigation *                                   550,000           15,285

                                                                         64,345


Internet Software & Services   1.1%

Autobytel *                                          1,000,000            9,080

Digital Insight *                                      950,000           19,693

MatrixOne *                                          1,225,000            8,465

Netegrity *                                          1,200,000           10,152

Sonicwall *                                            850,000            7,310

The Knot *!                                          1,350,000            5,468

                                                                         60,168

IT Services   2.6%

BISYS Group *                                        2,000,000           28,120

Certegy                                              1,100,000           42,680

Global Payments                                        500,000           22,510

Maximus *                                              350,000           12,411

META Group *!                                        1,000,000            3,910

Paychex                                                100,000            3,388

SkillSoft ADR *                                      3,250,000           24,700

SRA International, Class A *                           100,000            4,232

                                                                        141,951


Semiconductor & Semiconductor Equipment   6.2%

Altera *                                               600,000           13,332

AMIS Holdings *                                      1,250,000           21,150

Analog Devices                                         750,000           35,310

Artisan Components *                                   375,000            9,675

Atheros Communications *                               400,000            4,216

ATMI *                                               1,100,000           30,041

Cabot Microelectronics *                               300,000            9,183

Cognex                                                 350,000           13,468




Integrated Circuit Systems *                         1,000,000           27,160

Intersil Holding, Class A                            1,050,000           22,743

Intevac *                                              400,000            3,548

Lattice Semiconductor *                                700,000            4,907

Linear Technology                                      200,000            7,894

Maxim Integrated Products                              750,000           39,316

Micrel *                                               725,000            8,809

Microsemi *                                          1,000,000           14,210

MKS Instruments *                                      450,000           10,269

PDF Solutions *                                        400,000            3,388

Semtech *                                              825,000           19,420

Sigmatel *                                             266,700            7,750

Tessera Technologies *                                 500,000            9,010

Xilinx                                                 500,000           16,655

                                                                        331,454


Software   8.7%

Actuate *                                              900,000            3,555

Agile Software *!                                    2,850,000           24,937

Altiris *                                              707,300           19,529

Business Objects ADR *                                 450,000           10,184

Cadence Design Systems *                               500,000            7,315

Concord Communications *                               675,000            7,702

Convera *                                            1,500,000            3,465

FactSet Research Systems                               500,000           23,635

FileNet *                                              600,000           18,942

Informatica *                                        4,100,000           31,283

Internet Security Systems *                            600,000            9,204

Jack Henry & Associates                              1,625,000           32,662

Kronos *                                             1,050,000           43,260

Macromedia *                                         1,200,000           29,460

Magma Design Automation *                              600,000           11,538

Mercury Interactive *                                  650,000           32,389

Motive *                                               609,900            6,294

Nassda *                                               850,000            3,519

NetIQ *                                              1,750,000           23,100

Network Associates *                                 1,425,000           25,835




Open Solutions *                                       410,893           10,264

Quest Software *                                       800,000           10,320

Red Hat *                                            1,000,000           22,970

RSA Security *                                         725,000           14,841

Salesforce.com *                                       262,000            4,210

TALX Corporation                                       550,000           13,437

Verisity Ltd. *                                        175,000            1,050

Verity *                                             1,450,000           19,590

                                                                        464,490

Total Information Technology                                          1,153,098


MATERIALS   1.2%

Chemicals   0.6%

Airgas                                                 400,000            9,564

Symyx Technologies *                                 1,000,000           24,120

                                                                         33,684


Metals & Mining   0.6%

Steel Dynamics *                                     1,000,000           28,630

                                                                         28,630

Total Materials                                                          62,314


TELECOMMUNICATION SERVICES   4.2%

Wireless Telecommunication Services   4.2%

@Road *                                                500,000            3,825

Crown Castle International *                         1,000,000           14,750

Millicom International Cellular *                      600,000           13,116

Nextel Partners, Class A *                           2,850,000           45,372

NII Holdings, Class B *                              2,250,000           75,802

Triton PCS Holdings, Class A *                         636,900            2,777

Western Wireless, Class A *                          2,000,000           57,820

Wireless Facilities *                                1,400,000           13,762

Total Telecommunication Services                                        227,224


Total Equity Investments (Cost  $3,585,064)                           5,349,975





SHORT-TERM INVESTMENTS   0.8%

Money Market Fund   0.8%

T. Rowe Price Reserve Investment Fund, 1.16% #      44,557,447           44,557

Total Short-Term Investments (Cost $44,557)                              44,557

Total Investments in Securities

100.4% of Net Assets (Cost $3,629,621)                               $5,394,532
                                                                     ----------

(1)  Denominated in U.S. dollars unless otherwise noted

#    Seven-day yield

*    Non-income producing

(s.) Common stocks, rights, and warrants - cost $3,576,444, value $5,343,355,
     99.5% of net assets; Preferred stocks - cost $4,620, value $4,620, 0.1% of
     net assets; Convertible preferred stocks - cost $4,000, value $2,000, 0% of
     net assets

!    Affiliated company - See Note 2.

!!   Security contains restrictions as to public resale pursuant to the
     Securities Act of 1933 and related rules - total value of such securities
     at period-end amounts to $6,620 and represents 0.1% of net assets

@    Valued by the T. Rowe Price Valuation Committee, established by the fund's
     Board of Directors

ADR  American Depository Receipts


The accompanying notes are an integral part of these financial statements.



T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)                           June 30, 2004

STATEMENT OF ASSETS AND LIABILITIES
- --------------------------------------------------------------------------------
(In thousands except shares and per share amounts)

Assets

Investments in securities, at value

  Affiliated companies (cost $243,691)                            $     305,807

  Other companies (cost $3,385,930)                                   5,088,725

Total investments in securities                                       5,394,532

Other assets                                                             32,783

Total assets                                                          5,427,315

Liabilities

Total liabilities                                                        56,419

NET ASSETS                                                        $   5,370,896
                                                                  -------------

Net Assets Consist of:

Undistributed net investment income (loss)                        $     (18,236)

Undistributed net realized gain (loss)                                  (36,477)

Net unrealized gain (loss)                                            1,764,911

Paid-in-capital applicable to 201,735,292 shares of
$1.00 par value capital stock outstanding;
300,000,000 shares authorized                                         3,660,698

NET ASSETS                                                        $   5,370,896
                                                                  -------------

NET ASSET VALUE PER SHARE                                         $       26.62
                                                                  -------------

The accompanying notes are an integral part of these financial statements.



T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)

STATEMENT OF OPERATIONS
- --------------------------------------------------------------------------------
($ 000s)
                                                                       6 Months
                                                                          Ended
                                                                        6/30/04
Investment Income (Loss)

Dividend income                                                   $       4,766

Expenses

  Investment management                                                  17,498

  Shareholder servicing                                                   5,203

  Custody and accounting                                                    143

  Prospectus and shareholder reports                                         58

  Legal and audit                                                            56

  Registration                                                               34

  Directors                                                                   6

  Miscellaneous                                                               5

  Total expenses                                                         23,003

  Expenses paid indirectly                                                   (1)

  Net expenses                                                           23,002

Net investment income (loss)                                            (18,236)

Realized and Unrealized Gain (Loss)

Net realized gain (loss) on securities                                  219,046

Change in net unrealized gain (loss) on securities                      161,025

Net realized and unrealized gain (loss)                                 380,071

INCREASE (DECREASE) IN NET
ASSETS FROM OPERATIONS                                            $     361,835
                                                                  -------------

The accompanying notes are an integral part of these financial statements.


T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)

STATEMENT OF CHANGES IN NET ASSETS
- --------------------------------------------------------------------------------
($ 000s)
                                                       6 Months            Year
                                                          Ended           Ended
                                                        6/30/04        12/31/03
Increase (Decrease) in Net Assets

Operations

  Net investment income (loss)                      $   (18,236)    $   (30,379)

  Net realized gain (loss)                              219,046         115,336

  Change in net unrealized gain (loss)                  161,025       1,545,443

  Increase (decrease) in net assets from operations     361,835       1,630,400

Capital share transactions *

  Shares sold                                           527,219         794,491

  Distributions reinvested                                    -              10

  Shares redeemed                                      (473,234)       (829,181)

  Increase (decrease) in net assets from capital
  share transactions                                     53,985         (34,680)

Net Assets

Increase (decrease) during period                       415,820       1,595,720

Beginning of period                                   4,955,076       3,359,356

End of period                                       $ 5,370,896     $ 4,955,076
                                                    -----------     -----------

(Including undistributed net investment
income (loss) of $(18,236) at 6/30/04
and $0 at 12/31/03)

*Share information

  Shares sold                                            20,065          38,617

  Shares redeemed                                       (18,114)        (41,135)

  Increase (decrease) in shares outstanding               1,951          (2,518)

The accompanying notes are an integral part of these financial statements.



T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report (Unaudited)                           June 30, 2004

NOTES TO FINANCIAL STATEMENTS
- --------------------------------------------------------------------------------

NOTE 1 - SIGNIFICANT ACCOUNTING POLICIES

T. Rowe Price New Horizons Fund, Inc. (the fund) is registered under the
Investment Company Act of 1940 (the 1940 Act) as a diversified, open-end
management investment company and commenced operations on June 3, 1960. The fund
seeks long-term capital growth by investing primarily in common stocks of small,
rapidly growing companies.

The accompanying financial statements were prepared in accordance with
accounting principles generally accepted in the United States of America, which
require the use of estimates made by fund management.

Valuation
The fund values its investments and computes its net asset value per share at
the close of the New York Stock Exchange (NYSE), normally 4 p.m. ET, each day
that the NYSE is open for business. Equity securities listed or regularly traded
on a securities exchange or in the over-the-counter market are valued at the
last quoted sale price or, for certain markets, the official closing price at
the time the valuations are made, except for OTC Bulletin Board securities,
which are valued at the mean of the latest bid and asked prices. A security that
is listed or traded on more than one exchange is valued at the quotation on the
exchange determined to be the primary market for such security. Listed
securities not traded on a particular day are valued at the mean of the latest
bid and asked prices for domestic securities and the last quoted sale price for
international securities.

Debt securities are generally traded in the over-the-counter market. Securities
with original maturities of one year or more are valued at prices furnished by
dealers who make markets in such securities or by an independent pricing
service, which considers yield or price of bonds of comparable quality, coupon,
maturity, and type, as well as prices quoted by dealers who make markets in such
securities. Securities with original maturities of less than one year are valued
at amortized cost in local currency, which approximates fair value when combined
with accrued interest.

Investments in mutual funds are valued at the mutual fund's closing net asset
value per share on the day of valuation.




Other investments and those for which the above valuation procedures are
inappropriate or are deemed not to reflect fair value are stated at fair value
as determined in good faith by the T. Rowe Price Valuation Committee,
established by the fund's Board of Directors.

Rebates and Credits
Subject to best execution, the fund may direct certain security trades to
brokers who have agreed to rebate a portion of the related brokerage commission
to the fund in cash. Commission rebates are included in realized gain on
securities in the accompanying financial statements and totaled $124,000 for the
six months ended June 30, 2004. Additionally, the fund earns credits on
temporarily uninvested cash balances at the custodian that reduce the fund's
custody charges. Custody expense in the accompanying financial statements is
presented before reduction for credits, which are reflected as expenses paid
indirectly.

Investment Transactions, Investment Income, and Distributions
Income and expenses are recorded on the accrual basis. Dividends received from
mutual fund investments are reflected as dividend income; capital gain
distributions are reflected as realized gain/loss. Dividend income and capital
gain distributions are recorded on the ex-dividend date. Investment transactions
are accounted for on the trade date. Realized gains and losses are reported on
the identified cost basis. Distributions to shareholders are recorded on the
ex-dividend date. Income distributions are declared and paid on an annual basis.
Capital gain distributions, if any, are declared and paid by the fund, typically
on an annual basis.

Other
In the normal course of business, the fund enters into contracts that provide
general indemnifications. The fund's maximum exposure under these arrangements
is dependent on claims that may be made against the fund in the future and,
therefore, cannot be estimated; however, based on experience, the risk of
material loss from such claims is considered remote.


NOTE 2 - INVESTMENT TRANSACTIONS

Consistent with its investment objective, the fund engages in the following
practices to manage exposure to certain risks or enhance performance. The
investment objective, policies, program, and risk factors of the fund are
described more fully in the fund's prospectus and Statement of Additional
Information.




Affiliated Companies
The fund may invest in certain securities that are considered affiliated
companies. As defined by the 1940 Act, an affiliated company is one in which the
fund owns 5% or more of the outstanding voting securities. At June 30, 2004, the
value of affiliated companies totaled $305,807,000, representing 5.7% of the
value of the fund's investments in securities. For the six months then ended,
$160,000 (3.4%) of dividend income, and $10,232,000 (4.7%) of net realized loss
reflected in the accompanying financial statements resulted from the fund's
transactions with affiliated companies.

Other
Purchases and sales of portfolio securities, other than short-term securities,
aggregated $797,783,000 and $757,784,000, respectively, for the six months ended
June 30, 2004.


NOTE 3 - FEDERAL INCOME TAXES

No provision for federal income taxes is required since the fund intends to
continue to qualify as a regulated investment company under Subchapter M of the
Internal Revenue Code and distribute to shareholders all of its taxable income
and gains. Federal income tax regulations differ from generally accepted
accounting principles; therefore, distributions determined in accordance with
tax regulations may differ in amount or character from net investment income and
realized gains for financial reporting purposes. Financial reporting records are
adjusted for permanent book/tax differences to reflect tax character. Financial
records are not adjusted for temporary differences. The amount and character of
tax-basis distributions and composition of net assets are finalized at fiscal
year-end; accordingly, tax-basis balances have not been determined as of June
30, 2004.

For tax purposes, the fund has elected to treat net capital losses realized
between November 1 and December 31 of each year as occurring on the first day of
the following tax year; consequently, $7,117,000 of realized losses recognized
for financial reporting purposes in the year ended December 31, 2003 were
recognized for tax purposes on January 1, 2004. Further, the fund intends to
retain realized gains to the extent of available capital loss carryforwards. As
of December 31, 2003, the fund had $248,406,000 of unused capital loss
carryforwards, of which $34,264,000 expire in 2009, and $214,142,000 expire in
2010.




At June 30, 2004, the cost of investments for federal income tax purposes was
$3,629,621,000. Net unrealized gain aggregated $1,764,911,000 at period-end, of
which $2,127,134,000 related to appreciated investments and $362,223,000 related
to depreciated investments.


NOTE 4 - RELATED PARTY TRANSACTIONS

The fund is managed by T. Rowe Price Associates, Inc. (the manager or Price
Associates), a wholly owned subsidiary of T. Rowe Price Group, Inc. The
investment management agreement between the fund and the manager provides for an
annual investment management fee, which is computed daily and paid monthly. The
fee consists of an individual fund fee, equal to 0.35% of the fund's average
daily net assets, and the fund's pro-rata share of a group fee. The group fee is
calculated based on the combined net assets of certain mutual funds sponsored by
Price Associates (the group) applied to a graduated fee schedule, with rates
ranging from 0.48% for the first $1 billion of assets to 0.295% for assets in
excess of $120 billion. The fund's portion of the group fee is determined by the
ratio of its average daily net assets to those of the group. At June 30, 2004,
the effective annual group fee rate was 0.31%, and investment management fee
payable totaled $2,903,000.

In addition, the fund has entered into service agreements with Price Associates
and two wholly owned subsidiaries of Price Associates (collectively, Price).
Price Associates computes the daily share price and maintains the financial
records of the fund. T. Rowe Price Services, Inc., provides shareholder and
administrative services in its capacity as the fund's transfer and dividend
disbursing agent. T. Rowe Price Retirement Plan Services, Inc., provides
subaccounting and recordkeeping services for certain retirement accounts
invested in the fund. Expenses incurred pursuant to these service agreements
totaled $3,789,000 for the six months ended June 30, 2004, of which $623,000 was
payable at period-end.

The fund is also one of several mutual funds sponsored by Price Associates
(underlying Price funds) in which the T. Rowe Price Spectrum Funds (Spectrum
Funds) may invest. The Spectrum Funds do not invest in the underlying Price
funds for the purpose of exercising management or control. Pursuant to a special
servicing agreement, expenses associated with the operation of the




Spectrum Funds are borne by each underlying Price fund to the extent of
estimated savings to it and in proportion to the average daily value of its
shares owned by the Spectrum Funds. Expenses allocated under this agreement are
reflected as shareholder servicing expense in the accompanying financial
statements. For the six months ended June 30, 2004, the fund was allocated
$411,000 of Spectrum Funds' expenses, of which $298,000 related to services
provided by Price and $58,000 was payable at period-end. At June 30, 2004,
approximately 7.3% of the outstanding shares of the fund were held by the
Spectrum Funds.

The fund may invest in the T. Rowe Price Reserve Investment Fund and the T. Rowe
Price Government Reserve Investment Fund (collectively, the Reserve Funds),
open-end management investment companies managed by Price Associates. The
Reserve Funds are offered as cash management options to mutual funds, trusts,
and other accounts managed by Price Associates and/or its affiliates, and are
not available for direct purchase by members of the public. The Reserve Funds
pay no investment management fees. During the six months ended June 30, 2004,
dividend income from the Reserve Funds totaled $179,000.




T. Rowe Price New Horizons Fund
- --------------------------------------------------------------------------------
Certified Semiannual Report

INFORMATION ON PROXY VOTING
- --------------------------------------------------------------------------------

A description of the policies and procedures that the T. Rowe Price New Horizons
Fund uses to determine how to vote proxies relating to portfolio securities is
available, without charge, upon request by calling 1-800-225-5132. It also
appears in the fund's Statement of Additional Information (Form 485B), which can
be found on the SEC's Web site, www.sec.gov.

Item 2.  Code of Ethics.

A code of ethics, as defined in Item 2 of Form N-CSR, applicable to its
principal executive officer, principal financial officer, principal accounting
officer or controller, or persons performing similar functions is filed as an
exhibit to the registrant's annual Form N-CSR. No substantive amendments were
approved or waivers were granted to this code of ethics during the registrant's
most recent fiscal half-year.

Item 3.  Audit Committee Financial Expert.

Disclosure required in registrant's annual Form N-CSR.

Item 4.  Principal Accountant Fees and Services.

Disclosure required in registrant's annual Form N-CSR.

Item 5.  Audit Committee of Listed Registrants.

Not applicable.

Item 6.  Schedule of Investments.

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

Not applicable.

Item 9. Submission of Matters to a Vote of Security Holders.

Not applicable.

Item 10. Controls and Procedures.

(a) The registrant's principal executive officer and principal financial officer
have evaluated the registrant's disclosure controls and procedures within 90
days of this filing and have concluded that the registrant's disclosure controls
and procedures were effective, as of that date, in ensuring that information
required to be disclosed by the registrant in this Form N-CSR was recorded,
processed, summarized, and reported timely.

(b) The registrant's principal executive officer and principal financial officer
are aware of no changes in the registrant's internal control over financial
reporting that occurred during the registrant's most recent fiscal half-year
that has materially affected, or is reasonably likely to materially affect, the
registrant's internal control over financial reporting.

Item 11. Exhibits.

(a)(1) The registrant's code of ethics pursuant to Item 2 of Form N-CSR is filed
with the registrant's annual Form N-CSR.

     (2) Separate certifications by the registrant's principal executive officer
and principal financial officer, pursuant to Section 302 of the Sarbanes-Oxley
Act of 2002 and required by Rule 30a-2(a) under the Investment Company Act of
1940, are attached.

     (3) Written solicitation to repurchase securities issued by closed-end
companies: 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 required by Rule 30a-2(b) under the Investment Company Act of 1940,
is attached.

                                   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.


T. Rowe Price New Horizons Fund, Inc.


By:      /s/ James S. Riepe
         James S. Riepe
         Principal Executive Officer

Date:    August 16, 2004


         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/ James S. Riepe
         James S. Riepe
         Principal Executive Officer

Date:    August 16, 2004


By:      /s/ Joseph A. Carrier
         Joseph A. Carrier
         Principal Financial Officer

Date:    August 16, 2004