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: 811-03326

Morgan Stanley U.S. Government Money Market Trust
(Exact name of registrant as specified in charter)

1221 Avenue of the Americas, New York, New York 10020
(Address of principal executive offices) (Zip code)

Ronald E. Robison
1221 Avenue of the Americas, New York, New York 10020
(Name and address of agent for service)

Registrant's telephone number, including area code: 212-762-4000

Date of fiscal year end: January 31, 2007

Date of reporting period: July 31, 2006

Item 1 - Report to Shareholders

Welcome, Shareholder:

In this report, you'll learn about how your investment in Morgan Stanley U.S.
Government Money Market Trust performed during the semiannual period. We will
provide an overview of the market conditions, and discuss some of the factors
that affected performance during the reporting period. In addition, this report
includes the Fund's financial statements and a list of Fund investments.

THIS MATERIAL MUST BE PRECEDED OR ACCOMPANIED BY A PROSPECTUS FOR THE FUND BEING
OFFERED.

MARKET FORECASTS PROVIDED IN THIS REPORT MAY NOT NECESSARILY COME TO PASS. THERE
IS NO ASSURANCE THAT A MUTUAL FUND WILL ACHIEVE ITS INVESTMENT OBJECTIVE. AN
INVESTMENT IN A MONEY MARKET FUND IS NOT INSURED OR GUARANTEED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY. ALTHOUGH THE FUND
SEEKS TO PRESERVE THE VALUE OF AN INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE
TO LOSE MONEY BY INVESTING IN THE FUND. PLEASE SEE THE PROSPECTUS FOR MORE
COMPLETE INFORMATION ON INVESTMENT RISKS.

FUND REPORT

For the six months ended July 31, 2006

MARKET CONDITIONS

During the six-month period ended July 31, 2006, the Federal Open Market
Committee (the "Fed") continued the pattern of raising short-term rates it began
in June of 2004. Through 17 steps of 25 basis points each, including three
during the six months covered by this report, the Fed increased its target rate
for federal funds from 1.00 percent to 5.25 percent, a five-year high.

Short-term rates rose alongside the federal funds rate, providing increased
return opportunities for investors in money market funds.

PERFORMANCE ANALYSIS

As of July 31, 2006, Morgan Stanley U.S. Government Money Market Trust had net
assets of approximately $921 million and an average portfolio maturity of 26
days. For the six-month period ended July 31, 2006, the Fund provided a total
return of 2.08 percent. For the seven-day period ended July 31, 2006, the Fund
provided an effective annualized yield of 4.76 percent and a current yield of
4.65 percent, while its 30-day moving average yield for July was 4.59 percent.
Past performance is no guarantee of future results.

Our strategy in managing the Fund remained consistent with our long-term focus
on preservation of capital and liquidity. We adhered to a conservative approach
which emphasized high-quality money market obligations, while avoiding the use
of derivatives or structured notes that might fluctuate excessively with
changing interest rates.

We also took advantage of the rising yields available on the money market
securities over the course of the period. As short-term interest rates climbed,
we reinvested the proceeds of maturing short-term holdings into higher-yielding
securities. Should rates continue to rise during the months ahead, we intend to
continue with this approach.

There is no guarantee that any sectors mentioned will continue to perform as
discussed herein or that securities in such sectors will be held by the Fund in
the future.

<Table>
<Caption>
PORTFOLIO COMPOSITION

U.S. Government Agencies 87.7%
Repurchase Agreements 12.3
</Table>

<Table>
<Caption>
MATURITY SCHEDULE

1-30 Days 73.0%
31-60 Days 9.5
61-90 Days 9.7
91-120 Days 4.6
121+ Days 3.2
</Table>

Data as of July 31, 2006. Subject to change daily. All percentages for portfolio
composition and maturity schedule are as a percentage of total investments.
These data are provided for informational purposes only and should not be deemed
a recommendation to buy or sell the securities mentioned. Morgan Stanley is a
full-service securities firm engaged in securities trading and brokerage
activities, investment banking, research and analysis, financing and financial
advisory services.

INVESTMENT STRATEGY

THE FUND WILL INVEST IN HIGH QUALITY, SHORT-TERM U.S. GOVERNMENT SECURITIES. THE
FUND'S "INVESTMENT ADVISER," MORGAN STANLEY INVESTMENT ADVISORS INC., SEEKS TO
MAINTAIN THE FUND'S SHARE PRICE AT $1.00. THE SHARE PRICE REMAINING STABLE AT
$1.00 MEANS THAT THE FUND WOULD PRESERVE THE PRINCIPAL VALUE OF YOUR INVESTMENT.

AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FEDERAL DEPOSIT
INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY. ALTHOUGH THE FUND SEEKS TO
PRESERVE THE VALUE OF YOUR INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE TO LOSE
MONEY BY INVESTING IN THE FUND.

FOR MORE INFORMATION ABOUT PORTFOLIO HOLDINGS

EACH MORGAN STANLEY FUND PROVIDES A COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS IN
ITS SEMIANNUAL AND ANNUAL REPORTS WITHIN 60 DAYS OF THE END OF THE FUND'S SECOND
AND FOURTH FISCAL QUARTERS. THE SEMIANNUAL REPORTS AND THE ANNUAL REPORTS ARE
FILED ELECTRONICALLY WITH THE SECURITIES AND EXCHANGE COMMISSION (SEC) ON FORM
N-CSRS AND FORM N-CSR, RESPECTIVELY. MORGAN STANLEY ALSO DELIVERS THE SEMIANNUAL
AND ANNUAL REPORTS TO FUND SHAREHOLDERS AND MAKES THESE REPORTS AVAILABLE ON ITS
PUBLIC WEB SITE, WWW.MORGANSTANLEY.COM. EACH MORGAN STANLEY FUND ALSO FILES A
COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS WITH THE SEC FOR THE FUND'S FIRST AND
THIRD FISCAL QUARTERS ON FORM N-Q. MORGAN STANLEY DOES NOT DELIVER THE REPORTS
FOR THE FIRST AND THIRD FISCAL QUARTERS TO SHAREHOLDERS, NOR ARE THE REPORTS
POSTED TO THE MORGAN STANLEY PUBLIC WEB SITE. YOU MAY, HOWEVER, OBTAIN THE FORM
N-Q FILINGS (AS WELL AS THE FORM N-CSR AND N-CSRS FILINGS) BY ACCESSING THE
SEC'S WEB SITE, HTTP://WWW.SEC.GOV. YOU MAY ALSO REVIEW AND COPY THEM AT THE
SEC'S PUBLIC REFERENCE ROOM IN WASHINGTON, DC. INFORMATION ON THE OPERATION OF
THE SEC'S PUBLIC REFERENCE ROOM MAY BE OBTAINED BY CALLING THE SEC AT (800)
SEC-0330. YOU CAN ALSO REQUEST COPIES OF THESE MATERIALS, UPON PAYMENT OF A
DUPLICATING FEE, BY ELECTRONIC REQUEST AT THE SEC'S E-MAIL ADDRESS
(PUBLICINFO@SEC.GOV) OR BY WRITING THE PUBLIC REFERENCE SECTION OF THE SEC,
WASHINGTON, DC 20549-0102.

HOUSEHOLDING NOTICE

TO REDUCE PRINTING AND MAILING COSTS, THE FUND ATTEMPTS TO ELIMINATE DUPLICATE
MAILINGS TO THE SAME ADDRESS. THE FUND DELIVERS A SINGLE COPY OF CERTAIN
SHAREHOLDER DOCUMENTS, INCLUDING SHAREHOLDER REPORTS, PROSPECTUSES AND PROXY
MATERIALS, TO INVESTORS WITH THE SAME LAST NAME WHO RESIDE AT THE SAME ADDRESS.
YOUR PARTICIPATION IN THIS PROGRAM WILL CONTINUE FOR AN UNLIMITED PERIOD OF TIME
UNLESS YOU INSTRUCT US OTHERWISE. YOU CAN REQUEST MULTIPLE COPIES OF THESE
DOCUMENTS BY CALLING (800) 350-6414, 8:00 A.M. TO 8:00 P.M., ET. ONCE OUR
CUSTOMER SERVICE CENTER HAS RECEIVED YOUR INSTRUCTIONS, WE WILL BEGIN SENDING
INDIVIDUAL COPIES FOR EACH ACCOUNT WITHIN 30 DAYS.

EXPENSE EXAMPLE

As a shareholder of the Fund, you incur ongoing costs, including advisory 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 entire period 02/01/06 - 07/31/06.

ACTUAL EXPENSES

The first line of the table below 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 entitled "Expenses Paid During Period" to
estimate the expenses you paid on your account during this period.

HYPOTHETICAL EXAMPLE FOR COMPARISON PURPOSES

The second line of the table below provides information about 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 cost 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. Therefore, the second line of the table is useful in
comparing ongoing costs, and will not help you determine the relative total cost
of owning different funds that have transactional costs, such as sales charges
(loads), and redemption fees, or exchange fees.

<Table>
<Caption>
BEGINNING ENDING EXPENSES PAID
ACCOUNT VALUE ACCOUNT VALUE DURING PERIOD *
------------- ------------- ---------------
02/01/06 -
02/01/06 07/31/06 07/31/06
------------- ------------- ---------------

Actual (2.08% return)....................................... $1,000.00 $1,020.80 $3.71
Hypothetical (5% annual return before expenses)............. $1,000.00 $1,021.12 $3.71
</Table>

- ------------------

* Expenses are equal to the Fund's annualized expense ratio of 0.74%
multiplied by the average account value over the period, multiplied by
181/365 (to reflect the one-half year period). If the Fund had borne all of
its expenses, the annualized expense ratio would have been 0.75%.

INVESTMENT ADVISORY AGREEMENT APPROVAL

NATURE, EXTENT AND QUALITY OF SERVICES

The Board reviewed and considered the nature and extent of the investment
advisory services provided by the Investment Adviser under the Advisory
Agreement, including portfolio management, investment research and fixed income
securities trading. The Board also reviewed and considered the nature and extent
of the non-advisory, administrative services provided by the Fund's
Administrator under the Administration Agreement, including accounting,
clerical, bookkeeping, compliance, business management and planning, and the
provision of supplies, office space and utilities at the Investment Adviser's
expense. (The Investment Adviser and the Administrator together are referred to
as the "Adviser" and the Advisory and Administration Agreements together are
referred to as the "Management Agreement.") The Board also compared the nature
of the services provided by the Adviser with similar services provided by
non-affiliated advisers as reported to the Board by Lipper Inc. ("Lipper").

The Board reviewed and considered the qualifications of the portfolio managers,
the senior administrative managers and other key personnel of the Adviser who
provide the advisory and administrative services to the Fund. The Board
determined that the Adviser's portfolio managers and key personnel are well
qualified by education and/or training and experience to perform the services in
an efficient and professional manner. The Board concluded that the nature and
extent of the advisory and administrative services provided were necessary and
appropriate for the conduct of the business and investment activities of the
Fund. The Board also concluded that the overall quality of the advisory and
administrative services was satisfactory.

PERFORMANCE RELATIVE TO COMPARABLE FUNDS MANAGED BY OTHER ADVISERS

On a regular basis, the Board reviews the performance of all funds in the Morgan
Stanley Fund Complex, including the Fund, compared to their peers, paying
specific attention to the underperforming funds. In addition, the Board
specifically reviewed the Fund's performance for the one-, three- and five-year
periods ended November 30, 2005, as shown in a report provided by Lipper (the
"Lipper Report"), compared to the performance of comparable funds selected by
Lipper. The Board considered that adherence to the Fund's investment strategy
may result in periods of underperformance, but that, over time, adherence to the
Fund's investment strategy is appropriate. The Board concluded that the
performance of the Fund was acceptable.

FEES RELATIVE TO OTHER PROPRIETARY FUNDS MANAGED BY THE ADVISER WITH COMPARABLE
INVESTMENT STRATEGIES

The Board reviewed the advisory and administrative fee (together, the
"management fee") rate paid by the Fund under the Management Agreement. The
Board noted that the management fee rate was comparable to

the management fee rates charged by the Adviser to other proprietary funds it
manages with investment strategies comparable to those of the Fund.

FEES AND EXPENSES RELATIVE TO COMPARABLE FUNDS MANAGED BY OTHER ADVISERS

The Board reviewed the management fee rate and total expense ratio of the Fund
as compared to the average management fee rate and average total expense ratio
for funds, selected by Lipper (the "expense peer group"), managed by other
advisers with investment strategies comparable to those of the Fund, as shown in
the Lipper Report. The Board concluded that the Fund's management fee rate and
total expense ratio were competitive with those of its expense peer group.

BREAKPOINTS AND ECONOMIES OF SCALE

The Board reviewed the structure of the Fund's management fee schedule under the
Management Agreement and noted that it includes breakpoints. The Board also
reviewed the level of the Fund's management fee and noted that the fee, as a
percentage of the Fund's net assets, would decrease as net assets increase
because the management fee includes breakpoints. The Board concluded that the
Fund's management fee would reflect economies of scale as assets increase.

PROFITABILITY OF THE ADVISER AND AFFILIATES

The Board considered information concerning the costs incurred and profits
realized by the Adviser and affiliates during the last year from their
relationship with the Fund and during the last two years from their relationship
with the Morgan Stanley Fund Complex and reviewed with the Adviser the cost
allocation methodology used to determine the profitability of the Adviser and
affiliates. Based on its review of the information it received, the Board
concluded that the profits earned by the Adviser and affiliates were not
excessive in light of the advisory, administrative and other services provided
to the Fund.

FALL-OUT BENEFITS

The Board considered so-called "fall-out benefits" derived by the Adviser and
affiliates from their relationship with the Fund and the Morgan Stanley Fund
Complex, such as "float" benefits derived from handling of checks for purchases
and sales of Fund shares, through a broker-dealer affiliate of the Adviser. The
Board also considered that a broker-dealer affiliate of the Adviser receives
from the Fund 12b-1 fees for distribution and shareholder services. The Board
concluded that the float benefits were relatively small and the 12b-1 fees were
competitive with those of other broker-dealers.

SOFT DOLLAR BENEFITS

The Board considered whether the Adviser realizes any benefits from commissions
paid to brokers who execute securities transactions for the Fund ("soft
dollars"). The Board noted that the Fund invests only in fixed income
securities, which do not generate soft dollars.

ADVISER FINANCIALLY SOUND AND FINANCIALLY CAPABLE OF MEETING THE FUND'S NEEDS

The Board considered whether the Adviser is financially sound and has the
resources necessary to perform its obligations under the Management Agreement.
The Board noted that the Adviser's operations remain profitable, although
increased expenses in recent years have reduced the Adviser's profitability. The
Board concluded that the Adviser has the financial resources necessary to
fulfill its obligations under the Management Agreement.

HISTORICAL RELATIONSHIP BETWEEN THE FUND AND THE ADVISER

The Board also reviewed and considered the historical relationship between the
Fund and the Adviser, including the organizational structure of the Adviser, the
policies and procedures formulated and adopted by the Adviser for managing the
Fund's operations and the Board's confidence in the competence and integrity of
the senior managers and key personnel of the Adviser. The Board concluded that
it is beneficial for the Fund to continue its relationship with the Adviser.

OTHER FACTORS AND CURRENT TRENDS

The Board considered the controls and procedures adopted and implemented by the
Adviser and monitored by the Fund's Chief Compliance Officer and concluded that
the conduct of business by the Adviser indicates a good faith effort on its part
to adhere to high ethical standards in the conduct of the Fund's business.

GENERAL CONCLUSION

After considering and weighing all of the above factors, the Board concluded
that it would be in the best interest of the Fund and its shareholders to
approve renewal of the Management Agreement for another year.

Morgan Stanley U.S. Government Money Market Trust
PORTFOLIO OF INVESTMENTS - JULY 31, 2006 (UNAUDITED)

<Table>
<Caption>
ANNUALIZED
PRINCIPAL YIELD
AMOUNT IN ON DATE OF MATURITY
THOUSANDS DESCRIPTION PURCHASE DATE VALUE
- --------------------------------------------------------------------------------------------------------

U.S. Government Agency - Discount Notes (77.8%)
$ 11,949 Federal Farm Credit Banks.................. 5.15 % 08/01/06 $ 11,949,000
565,960 Federal Home Loan Banks.................... 5.05 - 5.36 08/01/06 - 10/25/06 564,367,677
111,830 Federal Home Loan Mortgage Corp. .......... 4.76 - 5.45 08/01/06 - 12/05/06 110,793,689
29,800 Federal National Mortgage Assoc. .......... 5.11 - 5.39 09/22/06 - 11/22/06 29,398,477
------------
Total U.S. Government Agency - Discount Notes (Cost $716,508,843)............ 716,508,843
------------
U.S. Government Agency - Floating Rate Notes (10.8%)
35,000 Federal Farm Credit Banks.................. 5.25 08/01/06 35,000,000
64,000 Federal Home Loan Banks.................... 5.03 - 5.27 08/02/06 - 08/21/06 63,999,959
------------
Total U.S. Government Agency - Floating Rate Notes (Cost $98,999,959)........ 98,999,959
------------
Repurchase Agreements (12.4%)
49,000 Barclays Capital Inc. (dated 07/31/06;
proceeds $49,007,200) (a)................ 5.29 08/01/06 49,000,000
25,000 Goldman Sachs & Co. (dated 07/21/06;
proceeds $25,076,563) (b)................ 5.25 08/11/06 25,000,000
25,000 Goldman Sachs & Co. (dated 07/18/06;
proceeds $25,110,104) (c)................ 5.29 08/17/06 25,000,000
15,000 Goldman Sachs & Co. (dated 07/24/06;
proceeds $15,066,438) (d)................ 5.32 08/23/06 15,000,000
------------
Total Repurchase Agreements (Cost $114,000,000).............................. 114,000,000
------------
</Table>

<Table>

Total Investments (Cost $929,508,802) (e)....................... 101.0% 929,508,802

Liabilities in Excess of Other Assets........................... (1.0) (8,971,723)
----- ------------
Net Assets...................................................... 100.0% $920,537,079
===== ============
</Table>

- ---------------------

<Table>

(a) Collateralized by Federal Mortgage Acceptance Corp. 6.00%
due 08/01/36 valued at $49,980,001.
(b) Collateralized by Federal National Mortgage Assoc.
4.00 - 8.00% due 11/01/12 - 07/01/36 valued at $18,532,839
and Federal Mortgage Acceptance Corp. 4.00 - 10.00% due
05/01/09 - 07/01/36 valued at $6,967,161.
(c) Collateralized by Federal National Mortgage Assoc.
4.00 - 8.50% due 11/01/08 - 07/01/36 valued at $19,251,530
and Federal Mortgage Acceptance Corp. 4.50 - 8.00% due
07/01/09 - 08/01/36 valued at $6,248,470.
(d) Collateralized by Federal National Mortgage Assoc.
4.00 - 9.25% due 04/01/09 - 07/01/36 valued $11,147,343
and Federal Mortgage Acceptance Corp. 4.50 - 10.00% due
10/01/08 - 06/01/36 valued at $4,152,657.
(e) Cost is the same for federal income tax purposes.
</Table>

See Notes to Financial Statements
8

Morgan Stanley U.S. Government Money Market Trust
FINANCIAL STATEMENTS

Statement of Assets and Liabilities
July 31, 2006 (unaudited)

<Table>

Assets:
Investments in securities, at value
(cost $929,508,802) (including
repurchase agreements of
$114,000,000)..................... $929,508,802
Cash................................ 74,553
Receivable for:
Interest........................ 533,185
Shares of beneficial interest
sold.......................... 3,669
Prepaid expenses and other assets... 47,242
------------
Total Assets.................... 930,167,451
------------
Liabilities:
Payable for:
Shares of beneficial interest
redeemed...................... 9,012,218
Investment advisory fee......... 315,447
Distribution fee................ 77,461
Transfer agent fee.............. 49,430
Administration fee.............. 38,730
Accrued expenses and other
payables.......................... 137,086
------------
Total Liabilities............... 9,630,372
------------
Net Assets...................... $920,537,079
============
Composition of Net Assets:
Paid-in-capital..................... $920,470,912
Accumulated undistributed net
investment income................. 65,373
Undistributed net realized gain..... 794
------------
Net Assets...................... $920,537,079
============
Net Asset Value Per Share
920,535,824 shares outstanding
(unlimited shares authorized of $.01
par value).......................... $1.00
============
</Table>

Statement of Operations
For the six months ended July 31, 2006 (unaudited)

<Table>

Net Investment Income:
Interest Income...................... $22,291,927
-----------
Expenses
Investment advisory fee.............. 1,857,895
Transfer agent fees and expenses..... 716,029
Distribution fee..................... 457,224
Administration fee................... 228,612
Shareholder reports and notices...... 49,476
Custodian fees....................... 24,721
Professional fees.................... 24,639
Registration fees.................... 22,614
Trustees' fees and expenses.......... 8,806
Other................................ 41,947
-----------
Total Expenses................... 3,431,963

Less: amounts waived................. (40,680)
Less: expense offset................. (6,353)
-----------
Net Expenses..................... 3,384,930
-----------
Net Investment Income............ 18,906,997
Net Realized Gain................ 794
-----------
Net Increase......................... $18,907,791
===========
</Table>

See Notes to Financial Statements
9

Morgan Stanley U.S. Government Money Market Trust
FINANCIAL STATEMENTS continued

Statements of Changes in Net Assets

<Table>
<Caption>
FOR THE SIX FOR THE YEAR
MONTHS ENDED ENDED
JULY 31, 2006 JANUARY 31, 2006
------------- ----------------
(unaudited)

Increase (Decrease) in Net Assets:
Operations:
Net investment income....................................... $ 18,906,997 $ 26,627,651
Net realized gain........................................... 794 --
------------ --------------
Net Increase............................................ 18,907,791 26,627,651
Dividends to shareholders from net investment income........ (18,928,031) (26,626,357)
Net decrease from transactions in shares of beneficial
interest.................................................. (17,267,939) (184,921,785)
------------ --------------
Net Decrease............................................ (17,288,179) (184,920,491)
Net Assets:
Beginning of period......................................... 937,825,258 1,122,745,749
------------ --------------
End of Period
(Including accumulated undistributed net investment income
of $65,373 and $86,407, respectively)....................... $920,537,079 $ 937,825,258
============ ==============
</Table>

10
See Notes to Financial Statements

Morgan Stanley U.S. Government Money Market Trust
NOTES TO FINANCIAL STATEMENTS - JULY 31, 2006 (UNAUDITED)

1. Organization and Accounting Policies

Morgan Stanley U.S. Government Money Market Trust (the "Fund") is registered
under the Investment Company Act of 1940, as amended (the "Act"), as a
diversified, open-end management investment company. The Fund's investment
objectives are security of principal, high current income and liquidity. The
Fund was organized as a Massachusetts business trust on November 18, 1981 and
commenced operations on February 17, 1982.

The following is a summary of significant accounting policies:

A. Valuation of Investments -- Portfolio securities are valued at amortized
cost, which approximates market value, in accordance with Rule 2a-7 under the
Act.

B. Accounting for Investments -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Discounts are accreted and premiums are amortized over the life of the
respective securities. Interest income is accrued daily.

C. Repurchase Agreements -- The Fund may invest directly with institutions in
repurchase agreements. The Fund's custodian receives the collateral, which is
marked-to-market daily to determine that the value of the collateral does not
decrease below the repurchase price plus accrued interest.

D. Federal Income Tax Policy -- It is the Fund's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute substantially all of its taxable income to its
shareholders. Accordingly, no federal income tax provision is required.

E. Dividends and Distributions to Shareholders -- The Fund records dividends and
distributions to shareholders as of the close of each business day.

F. Use of Estimates -- The preparation of financial statements in accordance
with generally accepted accounting principles requires management to make
estimates and assumptions that affect the reported amounts and disclosures.
Actual results could differ from those estimates.

2. Investment Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with Morgan Stanley Investment
Advisors Inc. (the "Investment Adviser"), the Fund pays the Investment Adviser
an advisory fee, accrued daily and payable monthly, by applying the following
annual rates to the net assets of the Fund determined as of the close of each
business day: 0.45% to the portion of the daily net assets not exceeding $500
million; 0.375% to the portion of the daily net assets exceeding $500 million
but not

Morgan Stanley U.S. Government Money Market Trust
NOTES TO FINANCIAL STATEMENTS - JULY 31, 2006 (UNAUDITED) continued

exceeding $750 million; 0.325% to the portion of the daily net assets exceeding
$750 million but not exceeding $1 billion; 0.30% to the portion of the daily net
assets exceeding $1 billion but not exceeding $1.5 billion; 0.275% to the
portion of the daily net assets exceeding $1.5 billion but not exceeding $2
billion; 0.25% to the portion of the daily net assets exceeding $2 billion but
not exceeding $2.5 billion; 0.225% to the portion of the daily net assets
exceeding $2.5 billion but not exceeding $3 billion; and 0.20% to the portion of
the daily net assets exceeding $3 billion.

Pursuant to an Administration Agreement with Morgan Stanley Services Company
Inc. (the "Administrator"), an affiliate of the Investment Adviser, the Fund
pays an administration fee, accrued daily and payable monthly, by applying the
annual rate of 0.05% to the Fund's daily net assets.

The Investment Adviser has voluntarily agreed to cap the Fund's operating
expenses through April 30, 2007, by assuming the Fund's "other expenses" and/or
waiving the Funds investment advisory fees, and the Fund's Administrator has
agreed to waive the administrative fees, to the extent such operating expenses
exceed 0.75% of the average net assets of the Fund on an annualized basis.

3. Plan of Distribution

Morgan Stanley Distributors Inc. (the "Distributor"), an affiliate of the
Investment Adviser and Administrator, is the distributor of the Fund's shares
and in accordance with a Plan of Distribution (the "Plan") pursuant to Rule
12b-1 under the Act, finances certain expenses in connection with the promotion
of sales of Fund shares.

Reimbursements for these expenses are made in monthly payments by the Fund to
the Distributor, which will in no event exceed an amount equal to a payment at
the annual rate of 0.15% of the Fund's average daily net assets during the
month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal
year will not be reimbursed by the Fund through payments accrued in any
subsequent fiscal year. For the six months ended July 31, 2006, the distribution
fee was accrued at the annual rate of 0.10%.

4. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales/maturities of portfolio securities
for the six months ended July 31, 2006 aggregated $23,569,281,152 and
$23,599,790,412, respectively.

Morgan Stanley Trust, an affiliate of the Investment Adviser, Administrator and
Distributor, is the Fund's transfer agent.

Morgan Stanley U.S. Government Money Market Trust
NOTES TO FINANCIAL STATEMENTS - JULY 31, 2006 (UNAUDITED) continued

The Fund has an unfunded noncontributory defined benefit pension plan covering
certain independent Trustees of the Fund who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on factors which include years of service and compensation. The
Trustees voted to close the plan to new participants and eliminate the future
benefits growth due to increases to compensation after July 31, 2003. Aggregate
pension costs for the six months ended July 31, 2006 included in Trustees' fees
and expenses in the Statement of Operations amounted to $709,676. At July 31,
2006, the Fund had an accrued pension liability of $63,177 which is included in
accrued expenses in the Statement of Assets and Liabilities.

The Fund has an unfunded Deferred Compensation Plan (the "Compensation Plan")
which allows each independent Trustee to defer payment of all, or a portion, of
the fees they receive for serving on the Board of Trustees. Each eligible
Trustee generally may elect to have their deferred amounts credited with a
return equal to the total return on one or more of the Morgan Stanley funds that
are offered as investment options under the Compensation Plan.
Appreciation/depreciation and distributions received from these investments are
recorded with an offsetting increase/decrease in the deferred compensation
obligation and do not affect the net asset value of the Fund.

5. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:

<Table>
<Caption>
FOR THE SIX FOR THE YEAR
MONTH ENDED ENDED
JULY 31, 2006 JANUARY 31, 2006
-------------- ----------------
(unaudited)

Shares sold................................................. 1,057,930,076 2,112,793,188
Shares issued in reinvestment of dividends.................. 18,845,936 26,500,899
-------------- --------------
1,076,776,012 2,139,294,087
Shares redeemed............................................. (1,094,043,951) (2,324,215,872)
-------------- --------------
Net decrease................................................ (17,267,939) (184,921,785)
============== ==============
</Table>

6. Expense Offset

The expense offset represents a reduction of the transfer agent fees and
expenses for earnings on cash balances maintained by the Fund.

7. Legal Matters

The Investment Adviser, certain affiliates of the Investment Adviser, certain
officers of such affiliates and certain investment companies advised by the
Investment Adviser or its affiliates, including the

Morgan Stanley U.S. Government Money Market Trust
NOTES TO FINANCIAL STATEMENTS - JULY 31, 2006 (UNAUDITED) continued

Fund, are named as defendants in a consolidated class action. This consolidated
action also names as defendants certain individual Trustees and Directors of the
Morgan Stanley funds. The consolidated amended complaint, filed in the United
States District Court Southern District of New York on April 16, 2004, generally
alleges that defendants, including the Fund, violated their statutory disclosure
obligations and fiduciary duties by failing properly to disclose (i) that the
Investment Adviser and certain affiliates of the Investment Adviser allegedly
offered economic incentives to brokers and others to recommend the funds advised
by the Investment Adviser or its affiliates to investors rather than funds
managed by other companies, and (ii) that the funds advised by the Investment
Adviser or its affiliates, including the Fund, allegedly paid excessive
commissions to brokers in return for their efforts to recommend these funds to
investors. The complaint seeks, among other things, unspecified compensatory
damages, rescissionary damages, fees and costs. The defendants have moved to
dismiss the action. On March 9, 2005, Plaintiffs sought leave to supplement
their complaint to assert claims on behalf of other investors, which motion
defendants opposed. On April 14, 2006, the Court granted defendants' motion to
dismiss in its entirety. Additionally, the Court denied Plaintiff's motion to
supplement their complaint. This matter is now concluded.

8. New Accounting Pronouncement

In July 2006, the Financial Accounting Standards Board (FASB) issued
Interpretation 48, Accounting for Uncertainty in Income Taxes -- an
interpretation of FASB Statement 109 (FIN 48). FIN 48 clarifies the accounting
for income taxes by prescribing the minimum recognition threshold a tax position
must meet before being recognized in the financial statements. FIN 48 is
effective for fiscal years beginning after December 15, 2006. The Fund will
adopt FIN 48 during 2007 and the impact to the Fund's financial statements, if
any, is currently being assessed.

Morgan Stanley U.S. Government Money Market Trust
FINANCIAL HIGHLIGHTS

Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:

<Table>
<Caption>
FOR THE SIX FOR THE YEAR ENDED JANUARY 31,
MONTHS ENDED ------------------------------------------------------------------------
JULY 31, 2006 2006 2005 2004 2003 2002
------------- -------- -------- -------- -------- --------
(unaudited)

Selected Per Share Data:
Net asset value, beginning of
period....................... $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00
------- ------- ------- ------- ------- -------
Net investment income from
investment operations........ 0.021 0.027 0.008 0.004 0.011 0.032
Less dividends from net
investment income............ (0.021) (0.027) (0.008) (0.004) (0.011) (0.032)
------- ------- ------- ------- ------- -------
Net asset value, end of
period....................... $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00
======= ======= ======= ======= ======= =======
Total Return.................. 2.08%(1) 2.71% 0.78% 0.45% 1.06% 3.25%
Ratios to Average Net Assets:
Total expenses (before expense
offset)...................... 0.74%(2)(3) 0.75%(3) 0.73% 0.71%(3) 0.74%(3) 0.74%(3)
Net investment income......... 4.14%(2)(3) 2.62%(3) 0.74% 0.43%(3) 1.03%(3) 3.14%(3)
Supplemental Data:
Net assets, end of period, in
millions..................... $921 $938 $1,123 $1,269 $1,340 $1,257
</Table>

- ---------------------

<Table>

(1) Not annualized.
(2) Annualized.
(3) If the Fund had borne all its expenses that were reimbursed or waived by the Investment Adviser and Administrator,
the annualized expense and net investment income ratios would have been as follows:

EXPENSE NET INVESTMENT
PERIOD ENDED RATIO INCOME RATIO
----------------- ---- ----
July 31, 2006 0.75% 4.13%
January 31, 2006 0.76 2.60
January 31, 2004 0.71 0.43
January 31, 2003 0.76 1.01
January 31, 2002 0.81 3.07
</Table>

15
See Notes to Financial Statements

TRUSTEES

Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
Wayne E. Hedien
James F. Higgins
Dr. Manuel H. Johnson
Joseph J. Kearns
Michael E. Nugent
Fergus Reid

OFFICERS

Michael E. Nugent
Chairman of the Board

Ronald E. Robison
President and Principal Executive Officer

J. David Germany
Vice President

Dennis F. Shea
Vice President

Barry Fink
Vice President

Amy R. Doberman
Vice President

Carsten Otto
Chief Compliance Officer

Stefanie V. Chang Yu
Vice President

Francis J. Smith
Treasurer and Chief Financial Officer

Mary E. Mullin
Secretary

TRANSFER AGENT

Morgan Stanley Trust
Harborside Financial Center, Plaza Two
Jersey City, New Jersey 07311

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

Deloitte & Touche LLP
Two World Financial Center
New York, New York 10281

INVESTMENT ADVISER

Morgan Stanley Investment Advisors Inc.
1221 Avenue of the Americas
New York, New York 10020

The financial statements included herein have been taken from the records of the
Fund without examination by the independent auditors and accordingly they do not
express an opinion thereon.

This report is submitted for the general information of the shareholders of the
Fund. For more detailed information about the Fund, its fees and expenses and
other pertinent information, please read its Prospectus. The Fund's Statement of
Additional Information contains additional information about the Fund, including
its trustees. It is available, without charge, by calling (800) 869-NEWS.

This report is not authorized for distribution to prospective investors in the
Fund unless preceded or accompanied by an effective Prospectus. Read the
Prospectus carefully before investing.
Investments and services offered through Morgan Stanley DW Inc., member SIPC.
Morgan Stanley Distributors Inc., member NASD.

[MORGAN STANLEY LOGO]

MORGAN STANLEY FUNDS

Morgan Stanley
U.S. Government
Money Market Trust

Semiannual Report
July 31, 2006

[MORGAN STANLEY LOGO]

DWGRPT-37960RPT-RA06-00818P-Y07/06

Item 2. Code of Ethics.