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: 811-06330

Morgan Stanley Limited Duration U.S. Government Trust

(Exact name of registrant as specified in charter)

522 Fifth Avenue, New York, New York 10036

(Address of principal executive offices) (Zip code)

Arthur Lev

522 Fifth Avenue, New York, New York 10036

(Name and address of agent for service)

Registrant’s telephone number, including area code: 201-830-8894

Date of fiscal year end: May 31, 2013

Date of reporting period: November 30, 2012

Item 1—Report to Shareholders

Trustees

Frank L. Bowman

Michael Bozic

Kathleen A. Dennis

James F. Higgins

Dr. Manuel H. Johnson

Joseph J. Kearns

Michael F. Klein

Michael E. Nugent

W. Allen Reed

Fergus Reid

Officers

Michael E. Nugent

Chairperson of the Board

Arthur Lev

President and Principal Executive Officer

Mary Ann Picciotto

Chief Compliance Officer

Stefanie V. Chang Yu

Vice President

Francis J. Smith

Treasurer and Principal Financial Officer

Mary E. Mullin

Secretary

Transfer Agent

Morgan Stanley Services Company Inc.

P.O. Box 219886

Kansas City, Missouri 64121

Custodian

State Street Bank and Trust Company

One Lincoln Street

Boston, Massachusetts 02111

Independent Registered Public Accounting Firm

Ernst & Young LLP

200 Clarendon Street

Boston, Massachusetts 02116

Legal Counsel

Dechert LLP

1095 Avenue of the Americas

New York, New York 10036

Counsel to the Independent Trustees

Kramer Levin Naftalis & Frankel LLP

1177 Avenue of the Americas

New York, New York 10036

Adviser

Morgan Stanley Investment Management Inc.

522 Fifth Avenue

New York, New York 10036

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. Please read the Prospectus carefully before investing.

Morgan Stanley Distribution, Inc., member FINRA.

© 2013 Morgan Stanley

MSLSAN

IU12-02732P-Y11/12

INVESTMENT MANAGEMENT

Morgan Stanley

Limited Duration U.S. Government Trust

Semiannual

Report

November 30, 2012

Morgan Stanley Limited Duration U.S. Government Trust

Table of Contents

Welcome Shareholder	3
Fund Report	4
Performance Summary	7
Expense Example	8
Investment Advisory Agreement Approval	9
Portfolio of Investments	12
Statement of Assets and Liabilities	16
Statement of Operations	16
Statements of Changes in Net Assets	17
Notes to Financial Statements	18
Financial Highlights	30
U.S. Privacy Policy	31

2

Welcome Shareholder,

We are pleased to provide this semiannual report, in which you will learn how your investment in Morgan Stanley Limited Duration U.S. Government Trust performed during the latest six-month period. It includes an overview of the market conditions and discusses some of the factors that affected performance during the reporting period. In addition, the report contains financial statements and a list of portfolio holdings.

Morgan Stanley Investment Management is a client-centric, investor-led organization. Our global presence, intellectual capital, and breadth of products and services enable us to partner with investors to meet the evolving challenges of today’s financial markets. We aim to deliver superior investment service and to empower our clients to make the informed decisions that help them reach their investment goals.

As always, we thank you for selecting Morgan Stanley Investment Management, and look forward to working with you in the months and years ahead.

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 the Fund will achieve its investment objective. The Fund is subject to market risk, which is the possibility that market values of securities owned by the Fund will decline and, therefore, the value of the Fund’s shares may be less than what you paid for them. Accordingly, you can lose money investing in this Fund. Please see the prospectus for more complete information on investment risks.

3

Fund Report (unaudited)

For the six months ended November 30, 2012

Total Return for the 6 Months Ended November 30, 2012

Morgan Stanley Limited Duration U.S. Government Trust		Barclays Capital 1-3 Year U.S. Government Bond Index1		Lipper Short U.S. Government Funds Index2
	0.32%		0.26%		0.52%

The Fund’s total return assumes the reinvestment of all distributions. See Performance Summary for standardized performance and benchmark information.

Market Conditions

Aggressive central bank policy actions to help support economic growth and provide stability led to a huge rally in risky assets so far in 2012. Given the weaker-than-expected economic conditions in the U.S., the Federal Reserve Bank enacted various easing policies during the course of the period. This included initiating another round of quantitative easing focused on mortgage purchases and extending the timeline to keep the target federal funds rate on hold until the unemployment rate falls to an acceptable level. The labor market in the U.S. showed improvement but unemployment remained high. The unemployment rate fell to 7.7 percent as of November 2012 from 8.3 percent at the beginning of the year, partly due to a drop in the labor participation rate. Economic growth in the U.S. remained sluggish as gross domestic product (GDP) growth over the past two quarters was about 2 percent.

Over the reporting period, the yield curve steepened as 2- and 5-year Treasury yields declined by 1 and 6 basis points, respectively, while 10- and 30-year yields increased by 3 and 12 basis points, respectively. The 10-year Treasury yield touched an all-time low of 1.43 percent in July.

Mortgage-backed securities performed relatively well over the period. The latest round of quantitative easing led to a substantial tightening in lower-coupon, fixed-rate mortgage spreads. Despite historically low mortgage rates, refinancing activity had been slower than it has been in the past under similar rate incentives, as many borrowers were unable to refinance due to tighter underwriting standards. However, with further quantitative easing, there has been an increase in mortgage refinancing. The U.S. housing market has also started showing signs of stabilization. After many months of continuous declines, the headline home price index turned positive on a year-over-year basis in June.

Performance Analysis

The Morgan Stanley Limited Duration U.S. Government Trust outperformed the Barclays Capital 1-3 Year U.S. Government Bond Index (the “Index”) and underperformed the Lipper Short U.S. Government Funds Index for the six months ended November 30, 2012.

The Fund’s allocation to agency mortgage-backed securities contributed to relative performance as mortgage spreads tightened during the period. A small underweight to agency debt detracted slightly from performance. However, this was offset by the portfolio’s allocation to agency commercial mortgage-backed securities, as the sector performed well with spreads narrowing over the past few months. Interest rate positioning did not have a material impact on performance.

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.

4

PORTFOLIO COMPOSITION* as of 11/30/12
U.S. Treasury Securities	36.7	%
Agency Fixed Rate Mortgages	24.2
Agency Bonds – Banking (FDIC Guaranteed)	16.0
Agency Adjustable Rate Mortgages	8.2
Short-Term Investments	8.1
Collateralized Mortgage Obligations – Agency Collateral Series	4.6
U.S. Agency Securities	1.1
Agency Bond – Consumer Discretionary (U.S. Government Guaranteed)	0.4
Sovereign	0.4
Asset-Backed Security	0.3

LONG-TERM CREDIT ANALYSIS as of 11/30/12
AAA	20.8	%
AA	77.4
Not Rated	1.8

* Does not include open short futures contracts with an underlying face amount of $46,360,313 with total unrealized depreciation of $21,049. Also does not include open swap agreements with total unrealized depreciation of $80,542.

Subject to change daily. Provided for informational purposes only and should not be deemed as a recommendation to buy or sell the securities mentioned above. All percentages for portfolio composition are as a percentage of total investments and all percentages for long-term credit analysis are as a percentage of total long-term investments.

Security ratings disclosed with the exception for those labeled “unrated’ have been rated by at least one Nationally Recognized Statistical Rating Organization (“NRSRO”). These ratings are obtained from Standard & Poor’s Ratings Group (“S&P”), Moody’s Investors Services, Inc (“Moody’s”) or Fitch Ratings (“Fitch”). If two or more NRSROs have assigned a rating to a security, the highest rating is used and if securities are unrated, the Adviser has deemed them to be of comparable quality. Ratings from Moody’s or Fitch, when used, are converted into their equivalent S&P rating.

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 invests substantially all of its net assets in securities issued by the U.S. Government, its agencies or instrumentalities, including U.S. Treasury securities and Treasury Inflation Protected Securities (“TIPS”), debt securities guaranteed under the Federal Deposit Insurance Corporation (“FDIC”) Temporary Liquidity Guarantee Program and other similar FDIC programs, and zero coupon securities. The Fund’s “Adviser,” Morgan Stanley Investment Management Inc., seeks to maintain an overall duration of the Fund’s portfolio of three years or less.

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)

5

or by writing the public reference section of the SEC, Washington, DC 20549-1520.

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) 869-NEWS, 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.

6

Performance Summary (unaudited)

Average Annual Total Returns — Period Ended November 30, 2012

Symbol	LDTRX
1 Year		1.15	%3
5 Years		2.36	3
10 Years		2.37	3
Since Inception (08/13/91)		3.91	3
Gross Expense Ratio		0.75	%

Performance data quoted represents past performance, which is no guarantee of future results and current performance may be lower or higher than the figures shown. For most recent month-end performance figures, please visit www.morganstanley.com/im or speak with your Financial Advisor. Investment returns and principal value will fluctuate and fund shares, when redeemed, may be worth more or less than their original cost. The table does not reflect the deduction of taxes that a shareholder would pay on fund distributions or the redemption of fund shares. Expense ratio is as of the Fund’s fiscal year end as outlined in the Fund’s current prospectus.

(1) The Barclays Capital 1-3 Year U.S. Government Bond Index is a sub-index of the Barclays Capital U.S. Government Bond Index and is comprised of Agency and Treasury securities with maturities of one to three years. The Index is unmanaged and its returns do not include any sales charges or fees. Such costs would lower performance. It is not possible to invest directly in an index.

(2) The Lipper Short U.S. Government Funds Index is an equally weighted performance index of the largest qualifying funds (based on net assets) in the Lipper Short U.S. Government Funds classification. The Index, which is adjusted for capital gains distributions and income dividends, is unmanaged and should not be considered an investment. There are currently 30 funds represented in this Index. The Fund was in the Lipper Short U.S. Government Funds classification as of the date of this report.

(3) Figure shown assumes reinvestment of all distributions. There are no sales charges.

7

Expense Example (unaudited)

As a shareholder of the Fund, you incur ongoing costs, including advisory fees; administration fees; shareholder services fee; 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.

This example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 06/01/12 – 11/30/12.

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.

Please note that “Expenses Paid During Period” are grossed up to reflect Fund expenses prior to the effect of Expense Offset (See Note 10 in the Notes to Financial Statements). Therefore, the annualized net expense ratios may differ from the ratio of expenses to average net assets shown in the Financial Highlights.

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) or exchange fees.

	Beginning Account Value		Ending Account Value		Expenses Paid During Period@
	06/01/12		11/30/12		06/01/12 – 11/30/12
Actual (0.32% return)	$	1,000.00	$	1,003.20	$	3.57
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,021.51	$	3.60

@ Expenses are equal to the Fund’s annualized expense ratio of 0.71% multiplied by the average account value over the period, multiplied by 183/365 (to reflect the one-half year period). If the fund had borne all of its expenses, the annualized expense ratio would have been 0.72%.

8

Investment Advisory Agreement Approval (unaudited)

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 (as defined herein) under the advisory agreement, including portfolio management, investment research and equity 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 (as defined herein) 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 and supported its decision to approve the Management Agreement.

Performance, Fees and Expenses of the Fund

The Board reviewed the performance, fees and expenses of the Fund compared to its peers, as determined by Lipper, and to appropriate benchmarks where applicable. The Board discussed with the Adviser the performance goals and the actual results achieved in managing the Fund. When considering a fund’s performance, the Board and the Adviser place emphasis on trends and longer-term returns (focusing on one-year, three-year and five-year performance, as of December 31, 2011, or since inception, as applicable). When a fund underperforms its benchmark and/or its peer group average, the Board and the Adviser discuss the causes of such underperformance and, where necessary, they discuss specific changes to investment strategy or investment personnel. The Board noted that the Fund’s performance was better than its peer group average for the one- and five-year periods but below its peer group average for the three-year period. The Board discussed with the Adviser the level of the advisory and administration fees (together, the “management fee”) for this Fund relative to comparable funds and/or other accounts advised by the Adviser and/or compared to its peers as determined by Lipper. In addition to the management fee, the Board also reviewed the Fund’s total expense ratio. The Board noted that the Fund’s management fee was lower than its

9

peer group average and the total expense ratio was higher but close to its peer group average. After discussion, the Board concluded that the Fund’s performance, management fee and total expense ratio were competitive with its peer group average.

Economies of Scale

The Board considered the size and growth prospects of the Fund and how that relates to the Fund’s total expense ratio and particularly the Fund’s management fee rate, which includes a breakpoint. In conjunction with its review of the Adviser’s profitability, the Board discussed with the Adviser how a change in assets can affect the efficiency or effectiveness of managing the Fund and whether the management fee level is appropriate relative to current and projected asset levels and/or whether the management fee structure reflects economies of scale as asset levels change. The Board has determined that its review of the actual and potential economies of scale of the Fund support its decision to approve the Management Agreement.

Profitability of the Adviser and Affiliates

The Board considered information concerning the costs incurred and profits realized by the Adviser and its 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. The Board has determined that its review of the analysis of the Adviser’s expenses and profitability supports its decision to approve the Management Agreement.

Other Benefits of the Relationship

The Board considered other benefits to the Adviser and its affiliates derived from their relationship with the Fund and other funds advised by the Adviser. These benefits may include, among other things, “float” benefits derived from handling of checks for purchases and sales, research received by the Adviser generated from commission dollars spent on funds’ portfolio trading and fees for distribution and/or shareholder servicing. The Board reviewed with the Adviser each of these arrangements and the reasonableness of the Adviser’s costs relative to the services performed. The Board has determined that its review of the other benefits received by the Adviser or its affiliates supports its decision to approve the Management Agreement.

Resources of the Adviser and Historical Relationship Between the Fund and the Adviser

The Board considered whether the Adviser is financially sound and has the resources necessary to perform its obligations under the Management Agreement. The Board also reviewed and considered the historical relationship between the Fund and the Adviser, including the organizational structure of the Adviser, the

10

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 the Adviser has the financial resources necessary to fulfill its obligations under the Management Agreement and 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. In reaching this conclusion the Board did not give particular weight to any single factor referenced above. The Board considered these factors over the course of numerous meetings, some of which were in executive session with only the independent Board members and their counsel present. It is possible that individual Board members may have weighed these factors differently in reaching their individual decisions to approve the Management Agreement.

11

Morgan Stanley Limited Duration U.S. Government Trust

Portfolio of Investments ⁿ November 30, 2012 (unaudited)

PRINCIPAL AMOUNT (000)			COUPON RATE	MATURITY DATE	VALUE
		Agency Adjustable Rate Mortgages (8.5%)
		Federal Home Loan Mortgage Corporation, Conventional Pools:
$	929		2.347%	06/01/38	$	998,458
	830		2.38	08/01/35		889,989
	1,142		2.455	01/01/36		1,217,960
	1,714		2.483	03/01/37		1,829,499
	291		2.758	07/01/36		310,983
	921		2.862	07/01/38		986,287
	1,266		2.911	09/01/35		1,342,759
	1,280		3.18	05/01/40		1,377,880
		Federal National Mortgage Association, Conventional Pools:
	910		2.332	05/01/35		971,309
	1,189		2.746	09/01/38		1,270,753
	1,469		2.88	10/01/37		1,580,091
	1,399		3.108	10/01/39		1,500,675
	1,077		3.327	05/01/39		1,160,710
	593		3.716	09/01/39		639,564
	691		4.291	07/01/39		742,838
	986		5.234	09/01/38		1,060,252
		Government National Mortgage Association, Various Pools:
	789		4.00	11/20/39 – 02/20/40		828,301
		Total Agency Adjustable Rate Mortgages (Cost $18,630,688)				18,708,308
		Agency Bonds – Banking (FDIC Guaranteed) (16.7%)
	13,745	Ally Financial, Inc.	2.20	12/19/12		13,755,762
	4,250	Citibank NA (See Note 6)	1.75	12/28/12		4,254,463
	4,100	Citigroup Funding, Inc. (See Note 6)	2.25	12/10/12		4,101,193
		General Electric Capital Corp.
	1,400		2.125	12/21/12		1,401,289
	6,470	Series G	2.625	12/28/12		6,480,559
	5,900	JPMorgan Chase & Co.	2.125	12/26/12		5,907,051
	880	NCUA Guaranteed Notes, Series A2	1.40	06/12/15		900,284
		Total Agency Bonds – Banking (FDIC Guaranteed) (Cost $37,082,620)				36,800,601
		Agency Bond – Consumer Discretionary (U.S. Government Guaranteed) (0.4%)
	926	Safina Ltd. (Cost $925,789)	2.00	12/30/23		953,298
		Agency Fixed Rate Mortgages (25.1%)
		Federal Home Loan Mortgage Corporation, December TBA:
	360		3.50	12/25/42(a)		383,006
		Gold Pools:
	388		3.50	08/01/42		414,165
	4,673		4.00	11/01/41 – 12/01/52		5,125,506

See Notes to Financial Statements

12

Morgan Stanley Limited Duration U.S. Government Trust

Portfolio of Investments ⁿ November 30, 2012 (unaudited)  continued

PRINCIPAL AMOUNT (000)			COUPON RATE	MATURITY DATE	VALUE
$	2,267		4.50  %	12/01/24	$	2,415,496
	86		7.50	05/01/35		106,014
	44		8.00	08/01/32		55,207
	47		8.50	08/01/31		59,079
		Federal National Mortgage Association, Conventional Pools:
	3,255		3.50	11/01/42 – 12/01/42		3,528,957
	8,041		4.00	06/01/24 – 12/01/41		8,621,412
	4,678		4.50	06/01/24 – 11/01/40		5,053,591
	8,343		5.00	12/01/23 – 01/01/41		9,159,449
	4,182		5.50	05/01/35 – 05/01/41		4,586,810
	1,116		6.00	02/01/37		1,237,795
	696		6.50	12/01/36		783,894
	732		7.00	04/01/32 – 03/01/37		872,621
	110		7.50	08/01/37		135,095
	200		8.00	04/01/33		248,139
	84		8.50	10/01/32		105,575
		December TBA:
	4,000		2.50	12/01/27(a)		4,185,000
		Government National Mortgage Association, December TBA:
	205		4.00	12/20/42(a)		224,379
		Various Pools:
	6,005		3.50	11/20/42		6,556,147
	507		6.00	11/15/38		568,912
	590		7.50	11/15/32		701,376
	389		8.50	07/15/30		455,054
		Total Agency Fixed Rate Mortgages (Cost $54,611,773)				55,582,679
		Asset-Backed Security (0.3%)
	730	United States Small Business Administration (Cost $730,000)	2.245	09/10/22		745,705
		Collateralized Mortgage Obligations – Agency Collateral Series (4.7%)
		Federal Home Loan Mortgage Corporation
	868		1.437	01/25/19		892,392
	362		1.56	10/25/18		372,558
	840		1.615	09/25/18		867,716
	1,600		1.655	11/25/16		1,655,956
	1,674		1.691	06/25/18		1,731,094
	1,013		1.776	04/25/18		1,049,215
	795		1.781	10/25/20		824,878
	373		1.873	01/25/18		386,364
	870		2.061	10/25/20		911,099
	689		2.257	10/25/20		727,098

See Notes to Financial Statements

13

Morgan Stanley Limited Duration U.S. Government Trust

Portfolio of Investments ⁿ November 30, 2012 (unaudited)  continued

PRINCIPAL AMOUNT (000)			COUPON RATE	MATURITY DATE	VALUE
$	555	Federal National Mortgage Association	0.953  %	11/25/15	$	561,576
	2,253	Government National Mortgage Association, IO	6.593(b)	08/16/36		489,789
		Total Collateralized Mortgage Obligations – Agency Collateral Series (Cost $10,002,568)				10,469,735
		Sovereign (0.4%)
	885	Tunisia Government AID Bonds (Cost $885,000)	1.686	07/16/19		884,604
		U.S. Agency Securities (1.2%)
	450	Federal Home Loan Mortgage Corporation	5.50	08/23/17		551,593
	1,540	Federal National Mortgage Association	0.875	10/26/17		1,554,542
	490	Private Export Funding Corp.	1.375	02/15/17		503,442
		Total U.S. Agency Securities (Cost $2,580,239)				2,609,577
		U.S. Treasury Securities (38.1%)
		U.S. Treasury Notes
	3,300		0.25	11/30/13		3,302,062
	14,000		0.50	10/15/14		14,064,540
	9,700		1.75	03/31/14		9,895,513
	14,000		1.875	04/30/14 – 06/30/15		14,515,626
	14,081		2.125	11/30/14		14,602,434
	21,450		2.25	05/31/14 – 01/31/15		22,239,191
	5,000		3.125	04/30/17		5,566,015
		Total U.S. Treasury Securities (Cost $83,360,288)				84,185,381
		Short-Term Investments (8.4%)
		U.S. Treasury Securities (2.4%)
		U.S. Treasury Bills
	1,740	(c)	0.117	02/14/13		1,739,796
	3,340	(c)	0.124	01/24/13		3,339,389
	240	(c)(d)	0.129	02/21/13		239,964
		Total U.S. Treasury Securities (Cost $5,318,902)				5,319,149

See Notes to Financial Statements

14

Morgan Stanley Limited Duration U.S. Government Trust

Portfolio of Investments ⁿ November 30, 2012 (unaudited)  continued

NUMBER OF SHARES (000)					VALUE
		Investment Company (6.0%)
	13,297	Morgan Stanley Institutional Liquidity Funds – Government Portfolio – Institutional Class (See Note 6) (Cost $13,297,267)			$	13,297,267
		Total Short-Term Investments (Cost $18,616,169)				18,616,416
		Total Investments (Cost $227,425,134) (e)	103.8	%		229,556,304
		Liabilities in Excess of Other Assets	(3.8	)		(8,415,436	)
		Net Assets	100.0	%	$	221,140,868

FDIC	Federal Deposit Insurance Corporation.
IO	Interest Only.
TBA	To Be Announced.
(a)	Security is subject to delayed delivery.
(b)	Variable/Floating Rate Security – Interest rate changes on these instruments are based on changes in a designated base rate. The rates shown are those in effect on November 30, 2012.
(c)	Rate shown is the yield to maturity at November 30, 2012.
(d)	All or a portion of this security has been physically segregated in connection with open futures contracts.
(e)	Securities are available for collateral in connection with securities purchased on a forward commitment basis, open futures contracts and swap agreements.

Futures Contracts Open at November 30, 2012:

NUMBER OF CONTRACTS		LONG/SHORT	DESCRIPTION, DELIVERY MONTH AND YEAR	UNDERLYING FACE AMOUNT AT VALUE	UNREALIZED DEPRECIATION
	5	Short	U.S. Treasury 30 yr. Bond, Mar–13	$  (750,312)	$	(2,539	)
	12	Short	U.S. Treasury 10 yr. Note, Mar–13	(1,603,688)		(4,424	)
	17	Short	U.S. Treasury 5 yr. Note, Mar–13	(2,120,219)		(5,180	)
	190	Short	U.S. Treasury 2 yr. Note, Mar–13	(41,886,094)		(8,906	)
			Total Unrealized Depreciation		$	(21,049	)

Interest Rate Swap Agreements Open at November 30, 2012:

SWAP COUNTERPARTY	NOTIONAL AMOUNT (000)		FLOATING RATE INDEX	PAY/RECEIVE FLOATING RATE	FIXED RATE	TERMINATION DATE		UNREALIZED DEPRECIATION
Credit Suisse	$	13,920	3-Month LIBOR	Receive	0.39%		09/25/14	$	(7,837	)
Deutsche Bank		11,000	3-Month LIBOR	Receive	0.83		09/21/17		(72,705	)
			Total Unrealized Depreciation					$	(80,542	)

LIBOR London Interbank Offered Rate.

See Notes to Financial Statements

15

Morgan Stanley Limited Duration U.S. Government Trust

Financial Statements

Statement of Assets and Liabilities

November 30, 2012 (unaudited)

Assets:
Investments in securities, at value (cost $205,702,199)	$	207,903,381
Investment in affiliates, at value (cost $21,722,935)		21,652,923
Total investments in securities, at value (cost $227,425,134)		229,556,304
Receivable for:
Investments sold		6,515,258
Interest and paydown		951,697
Shares of beneficial interest sold		302,726
Interest and dividends from affiliates		75,960
Prepaid expenses and other assets		9,482
Total Assets		237,411,427
Liabilities:
Unrealized depreciation on open swap agreements		80,542
Payable for:
Investments purchased		15,663,997
Shares of beneficial interest redeemed		218,614
Advisory fee		47,891
Shareholder services fee		45,722
Transfer agent fee		26,309
Dividends to shareholders		19,374
Administration fee		14,631
Variation margin		9,495
Accrued expenses and other payables		143,984
Total Liabilities		16,270,559
Net Assets	$	221,140,868
Composition of Net Assets:
Paid-in-capital	$	299,026,324
Net unrealized appreciation		2,029,579
Dividends in excess of net investment income		(971,715	)
Accumulated net realized loss		(78,943,320	)
Net Assets	$	221,140,868
Net Asset Value Per Share
23,812,686 shares outstanding (unlimited shares authorized of $0.01 par value)		$9.29

Statement of Operations

For the six months ended November 30, 2012 (unaudited)

Net Investment Income:
Income
Interest	$	1,275,458
Interest and dividends from affiliates (Note 6)		85,819
Total Income		1,361,277
Expenses
Advisory fee (Note 4)		287,896
Shareholder services fee (Note 5)		266,571
Administration fee (Note 4)		85,303
Professional fees		51,070
Transfer agent fees and expenses		29,394
Registration fees		14,212
Shareholder reports and notices		10,113
Custodian fees		9,731
Trustees’ fees and expenses		5,155
Other		7,836
Total Expenses		767,281
Less: rebate from Morgan Stanley affiliated cash sweep (Note 6)		(7,182	)
Net Expenses		760,099
Net Investment Income		601,178
Realized and Unrealized Gain (Loss):
Realized Gain (Loss) on:
Investments		533,573
Futures contracts		(293,720	)
Net Realized Gain		239,853
Change in Unrealized Appreciation (Depreciation) on:
Investments		(223,648	)
Investments in affiliates (Note 6)		(76,264	)
Futures contracts		143,445
Swap agreements		(80,542	)
Net Change in Unrealized Appreciation (Depreciation)		(237,009	)
Net Gain		2,844
Net Increase	$	604,022

See Notes to Financial Statements

16

Morgan Stanley Limited Duration U.S. Government Trust

Financial Statements  continued

Statements of Changes in Net Assets

	FOR THE SIX MONTHS ENDED NOVEMBER 30, 2012			FOR THE YEAR ENDED MAY 31, 2012
	(unaudited)
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	601,178		$	2,016,103
Net realized gain		239,853			2,093,244
Net change in unrealized depreciation		(237,009	)		(1,255,324	)
Net Increase		604,022			2,854,023
Dividends to shareholders from net investment income		(1,591,260	)		(3,627,398	)
Net increase (decrease) from transactions in shares of beneficial interest		17,032,038			(11,658,353	)
Net Increase (Decrease)		16,044,800			(12,431,728	)
Net Assets:
Beginning of period		205,096,068			217,527,796
End of Period
(Including dividends in excess of net investment income of $971,715 and accumulated undistributed net investment income of $18,367, respectively)	$	221,140,868		$	205,096,068

See Notes to Financial Statements

17

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)

1. Organization and Accounting Policies

Morgan Stanley Limited Duration U.S. Government 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 objective is to seek current income, preservation of principal and liquidity. The Fund was organized as a Massachusetts business trust on June 4, 1991 and commenced operations on August 13, 1991.

The following is a summary of significant accounting policies:

A. Valuation of Investments — (1) Certain portfolio securities may be valued by an outside pricing service approved by the Fund’s Board of Trustees (the “Trustees”). The prices provided by a pricing service take into account broker-dealer market price quotations for trading in similar groups of securities, security quality, maturity, coupon and other security characteristics as well as any developments related to the specific securities; (2) portfolio securities for which over-the-counter market quotations are readily available are valued at the mean between the last reported bid and asked price; (3) when market quotations are not readily available, including circumstances under which Morgan Stanley Investment Management Inc. (the “Adviser”), a wholly owned subsidiary of Morgan Stanley, determines that the market quotations are not reflective of a security’s fair value, portfolio securities are valued at their fair value as determined in good faith under procedures established by and under the general supervision of the Trustees; (4) futures are valued at the latest price published by the commodities exchange on which they trade; (5) swaps are marked-to-market daily based upon quotations from market makers; (6) investments in mutual funds, including the Morgan Stanley Institutional Liquidity Funds, are valued at the net asset value as of the close of each business day; and (7) short-term debt securities having a maturity date of more than sixty days at time of purchase are valued on a mark-to-market basis until sixty days prior to maturity and thereafter at amortized cost based on their value on the 61st day. Short-term debt securities having a maturity date of sixty days or less at the time of purchase are valued at amortized cost, which approximates fair value.

Under procedures approved by the Trustees, the Fund’s Adviser has formed a Valuation Committee. The Valuation Committee provides administration and oversight of the Fund’s valuation policies and procedures, which are reviewed at least annually by the Trustees. Among other things, these procedures allow the Fund to utilize independent pricing services, quotations from securities and financial instrument dealers, and other market sources to determine fair value.

The Fund has procedures to determine the fair value of securities and other financial instruments for which market prices are not readily available. Under these procedures, the Valuation Committee convenes on a regular and ad hoc basis to review such securities and considers a number of factors, including valuation methodologies and significant unobservable valuation inputs, when arriving at fair value. The Valuation Committee may employ a market-based approach which may use related or comparable assets or liabilities,

18

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

recent transactions, market multiples, book values, and other relevant information for the investment to determine the fair value of the investment. An income-based valuation approach may also be used in which the anticipated future cash flows of the investment are discounted to calculate fair value. Discounts may also be applied due to the nature or duration of any restrictions on the disposition of the investments. Due to the inherent uncertainty of valuations of such investments, the fair values may differ significantly from the values that would have been used had an active market existed. The Valuation Committee employs various methods for calibrating these valuation approaches including a regular review of valuation methodologies, key inputs and assumptions, transactional back-testing or disposition analysis, and reviews of any related market activity.

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. Dividend income and other distributions are recorded on the ex-dividend date. Discounts are accreted and premiums are amortized over the life of the respective securities and are included in interest income. Interest income is accrued daily as earned.

C. Dividends and Distributions to Shareholders — Dividends and distributions to shareholders are recorded on the ex-dividend date.

D. When-Issued/Delayed Delivery Securities — The Fund may purchase or sell when-issued and delayed delivery securities. Securities purchased on a when-issued or delayed delivery basis are purchased for delivery beyond the normal settlement date at a stated price and yield, and no income accrues to the Fund on such securities prior to delivery date. Payment and delivery for when-issued and delayed delivery securities can take place up to 120 days after the date of the transaction. When the Fund enters into a purchase transaction on a when-issued or delayed delivery basis, securities are available for collateral in an amount at least equal in value to the Fund’s commitments to purchase such securities. Purchasing securities on a when-issued or delayed delivery basis may involve a risk that the market price at the time of delivery may be lower than the agreed upon purchase price, in which case there could be an unrealized loss at the time of delivery. Purchasing investments on a when-issued or delayed delivery basis may be considered a form of leverage which may increase the impact that gains (losses) may have on the Fund.

E. Use of Estimates — The preparation of financial statements in accordance with generally accepted accounting principles in the United States (“GAAP”) requires management to make estimates and assumptions that affect the reported amounts and disclosures. Actual results could differ from those estimates.

F. Indemnifications — The Fund enters into contracts that contain a variety of indemnifications. The Fund’s maximum exposure under these arrangements is unknown. However, the Fund has not had prior claims or losses pursuant to these contracts and expects the risk of loss to be remote.

19

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

2. Fair Valuation Measurements

Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) 820, Fair Value Measurements and Disclosures (“ASC 820”), defines fair value as the value that the Fund would receive to sell an investment or pay to transfer a liability in a timely transaction with an independent buyer in the principal market, or in the absence of a principal market the most advantageous market for the investment or liability. ASC 820 establishes a three-tier hierarchy to distinguish between (1) inputs that reflect the assumptions market participants would use in valuing an asset or liability developed based on market data obtained from sources independent of the reporting entity (observable inputs); and (2) inputs that reflect the reporting entity’s own assumptions about the assumptions market participants would use in valuing an asset or liability developed based on the best information available in the circumstances (unobservable inputs) and to establish classification of fair value measurements for disclosure purposes. Various inputs are used in determining the value of the Fund’s investments. The inputs are summarized in the three broad levels listed below.

• Level 1 — unadjusted quoted prices in active markets for identical investments

• Level 2 — other significant observable inputs (including quoted prices for similar investments, interest rates, prepayment speeds, credit risk, etc.)

• Level 3 — significant unobservable inputs including the Fund’s own assumptions in determining the fair value of investments. Factors considered in making this determination may include, but are not limited to, information obtained by contacting the issuer, analysts, or the appropriate stock exchange (for exchange-traded securities), analysis of the issuer’s financial statements or other available documents and, if necessary, available information concerning other securities in similar circumstances

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities and the determination of the significance of a particular input to the fair value measurement in its entirety requires judgment and considers factors specific to each security.

20

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

The following is a summary of the inputs used to value the Fund’s investments as of November 30, 2012.

INVESTMENT TYPE	LEVEL 1 UNADJUSTED QUOTED PRICES			LEVEL 2 OTHER SIGNIFICANT OBSERVABLE INPUTS			LEVEL 3 SIGNIFICANT UNOBSERVABLE INPUTS		TOTAL
Assets:
Fixed Income Securities
Agency Adjustable Rate Mortgages	$	—		$	18,708,308		$	—	$	18,708,308
Agency Bonds – Banking (FDIC Guaranteed)		—			36,800,601			—		36,800,601
Agency Bond – Consumer Discretionary (U.S. Government Guaranteed)		—			953,298			—		953,298
Agency Fixed Rate Mortgages		—			55,582,679			—		55,582,679
Asset-Backed Security		—			745,705			—		745,705
Collateralized Mortgage Obligations – Agency Collateral Series		—			10,469,735			—		10,469,735
Sovereign		—			884,604			—		884,604
U.S. Agency Securities		—			2,609,577			—		2,609,577
U.S. Treasury Securities		—			84,185,381			—		84,185,381
Total Fixed Income Securities		—			210,939,888			—		210,939,888
Short-Term Investments
U.S. Treasury Securities		—			5,319,149			—		5,319,149
Investment Company		13,297,267			—			—		13,297,267
Total Short-Term Investments		13,297,267			5,319,149			—		18,616,416
Total Assets		13,297,267			216,259,037			—		229,556,304
Liabilities:
Futures Contracts		(21,049	)		—			—		(21,049	)
Interest Rate Swap Agreements		—			(80,542	)		—		(80,542	)
Total Liabilities		(21,049	)		(80,542	)		—		(101,591	)
Total	$	13,276,218		$	216,178,495		$	—	$	229,454,713

Transfers between investment levels may occur as the markets fluctuate and/or the availability of data used in an investment’s valuation changes. The Fund recognizes transfers between the levels as of the end of the period. As of November 30, 2012, the Fund did not have any investments transfer between investment levels.

3. Derivatives

The Fund may, but is not required to, use derivative instruments for a variety of purposes, including hedging, risk management, portfolio management or to earn income. Derivatives are financial instruments whose value is based on the value of an underlying asset, interest rate, index or financial instrument. A derivative instrument often has risks similar to its underlying asset and may have additional risks, including imperfect correlation between the value of the derivative and the underlying asset, risks of default by the counterparty to certain transactions, magnification of losses incurred due to changes in the market value of the securities,

21

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

instruments, indices or interest rates to which they relate, and risks that the transactions may not be liquid. The use of derivatives involves risks that are different from, and possibly greater than, the risks associated with other portfolio investments. Derivatives may involve the use of highly specialized instruments that require investment techniques and risk analyses different from those associated with other portfolio investments. All of the Fund’s holdings, including derivative instruments, are marked-to-market each day with the change in value reflected in unrealized appreciation (depreciation). Upon disposition, a realized gain or loss is recognized.

Certain derivative transactions may give rise to a form of leverage. Leverage magnifies the potential for gain and risk of loss. Leverage associated with derivative transactions may cause the Fund to liquidate portfolio positions when it may not be advantageous to do so to satisfy its obligations or to meet earmarking or segregation requirements, pursuant to applicable Securities and Exchange Commission rules and regulations, or may cause the Fund to be more volatile than if the Fund had not been leveraged. Although the Adviser seeks to use derivatives to further the Fund’s investment objectives, there is no assurance that the use of derivatives will achieve this result.

Following is a description of the derivative instruments and techniques that the Fund used during the period and their associated risks:

Futures    A futures contract is a standardized agreement between two parties to buy or sell a specific quantity of an underlying instrument at a specific price at a specific future time. The value of a futures contract tends to increase and decrease in tandem with the value of the underlying instrument. Depending on the terms of the particular contract, futures contracts are settled through either physical delivery of the underlying instrument on the settlement date or by payment of a cash settlement amount on the settlement date. During the period the futures contract is open, payments are received from or made to the broker based upon changes in the value of the contract (the variation margin). A decision as to whether, when and how to use futures involves the exercise of skill and judgment and even a well-conceived futures transaction may be unsuccessful because of market behavior or unexpected events. In addition to the derivatives risks discussed above, the prices of futures can be highly volatile, using futures can lower total return, and the potential loss from futures can exceed the Fund’s initial investment in such contracts.

Swaps    An over-the-counter (“OTC”) swap agreement is an agreement between two parties pursuant to which the parties exchange payments at specified dates on the basis of a specified notional amount, with the payments calculated by reference to specified securities, indexes, reference rates, currencies or other instruments. A small percentage of swap agreements are cleared through a central clearing house. Most swap agreements provide that when the period payment dates for both parties are the same, the payments are made on a net basis (i.e., the two payment streams are netted out, with only the net amount paid by one party to the other). The Fund’s obligations or rights under a swap agreement entered into on a net basis will

22

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

generally be equal only to the net amount to be paid or received under the agreement, based on the relative values of the positions held by each counterparty. Most swap agreements are not entered into or traded on exchanges and there is no central clearing or guaranty function for swaps. These OTC swaps are often subject to credit risk or the risk of default or non-performance by the counterparty. Swaps could result in losses if interest rate or foreign currency exchange rates or credit quality changes are not correctly anticipated by the Fund or if the reference index, security or investments do not perform as expected.

When the Fund has an unrealized loss on a swap agreement, the Fund has instructed the custodian to pledge cash or liquid securities as collateral with a value approximately equal to the amount of the unrealized loss. Collateral pledges are monitored and subsequently adjusted if and when the swap valuations fluctuate. If applicable, cash collateral is included with “Due from (to) broker” in the Statement of Assets and Liabilities.

FASB ASC 815, Derivatives and Hedging: Overall (“ASC 815”), is intended to improve financial reporting about derivative instruments by requiring enhanced disclosures to enable investors to better understand how and why the Fund uses derivative instruments, how these derivative instruments are accounted for and their effects on the Fund’s financial position and results of operations.

The following table sets forth the fair value of the Fund’s derivative contracts by primary risk exposure as of November 30, 2012.

PRIMARY RISK EXPOSURE	ASSET DERIVATIVES STATEMENT OF ASSETS AND LIABILITIES LOCATION	FAIR VALUE	LIABILITY DERIVATIVES STATEMENT OF ASSETS AND LIABILITIES LOCATION	FAIR VALUE
Interest Rate Risk	Variation margin	$        —	Variation margin	$	(21,049	)†
	Unrealized appreciation on open swap agreements	—	Unrealized depreciation on open swap agreements		(80,542	)
		$        —		$	(101,591	)

† Includes cumulative appreciation (depreciation) of futures contracts as reported in the Portfolio of Investments. Only current day’s net variation margin is reported within the Statement of Assets and Liabilities.

The following tables set forth by primary risk exposure the Fund’s realized gains (losses) and change in unrealized appreciation (depreciation) by type of derivative contract for the six months ended November 30, 2012 in accordance with ASC 815.

AMOUNT OF REALIZED GAIN (LOSS) ON DERIVATIVE CONTRACTS
PRIMARY RISK EXPOSURE	FUTURES
Interest Rate Risk	$	(293,720	)
CHANGE IN UNREALIZED APPRECIATION (DEPRECIATION) ON DERIVATIVE CONTRACTS
PRIMARY RISK EXPOSURE	FUTURES			SWAPS
Interest Rate Risk	$	143,445		$	(80,542	)

23

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

For the six months ended November 30, 2012, the average monthly original value of futures contracts was $62,589,153 and the average monthly notional value of swap agreements was $12,460,000.

4. Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with the Adviser, the Fund pays 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: 0.27% to the portion of the daily net assets not exceeding $1 billion and 0.25% to the portion of the daily net assets exceeding $1 billion. For the six months ended November 30, 2012, the advisory fee rate was equivalent to an annual effective rate of 0.26% of the Fund’s daily net assets.

Pursuant to an Administration Agreement with Morgan Stanley Services Company Inc. (the “Administrator”), an affiliate of the Adviser, the Fund pays an administration fee, accrued daily and payable monthly, by applying the annual rate of 0.08% to the Fund’s daily net assets.

Under a Sub-Administration Agreement between the Administrator and State Street Bank and Trust Company (“State Street”), State Street provides certain administrative services to the Fund. For such services, the Administrator pays State Street a portion of the fee the Administrator receives from the Fund.

5. Shareholder Services Plan

Pursuant to a Shareholder Services Plan (the “Plan”), the Fund may pay Morgan Stanley Distribution Inc. (the “Distributor”), an affiliate of the Adviser and Administrator, as compensation for the provision of services to shareholders a service fee up to the rate of 0.25% on an annualized basis of the average daily net assets of the Fund. For the six months ended November 30, 2012, the shareholder services fee was accrued at the annual rate of 0.25%.

6. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales of investment securities, excluding short-term investments, for the six months ended November 30, 2012, aggregated $200,853,303 and $200,821,939, respectively.

The Fund invests in the Institutional Class of the Morgan Stanley Institutional Liquidity Funds — Government Portfolio (the “Liquidity Funds”), an open-end management investment company managed by the Adviser. Advisory fees paid by the Fund are reduced by an amount equal to its pro-rata share of the advisory and administration fees paid by the Fund due to its investment in the Liquidity Funds. For the six months ended November 30, 2012, advisory fees paid were reduced by $7,182 relating to the Fund’s investment in the Liquidity Funds.

24

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

A summary of the Fund’s transactions in shares of the Liquidity Funds during the six months ended November 30, 2012 is as follows:

VALUE MAY 31, 2012		PURCHASES AT COST		SALES		DIVIDEND INCOME		VALUE NOVEMBER 30, 2012
$	4,348,726	$	71,104,734	$	62,156,193	$	2,507	$	13,297,267

The Fund had the following transactions with Citigroup, Inc., and its affiliated broker-dealers, which may be deemed to be affiliates of the Adviser, Administrator and Distributor under Section 17 of the Act, for the six months ended November 30, 2012:

VALUE MAY 31, 2012		PURCHASES AT COST	SALES	REALIZED GAIN	INTEREST INCOME		VALUE NOVEMBER 30, 2012
$	8,431,920	—	—	—	$	83,312	$	8,355,656

Morgan Stanley Services Company Inc., an affiliate of the Adviser and Distributor, is the Fund’s transfer agent.

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 November 30, 2012, included in “Trustees’ fees and expenses” in the Statement of Operations amounted to $2,057. At November 30, 2012, the Fund had an accrued pension liability of $58,122, which is included in “Accrued expenses and other payables” 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 he or she receives for serving on the Board of Trustees. Each eligible Trustee generally may elect to have the 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.

7. Purposes of and Risks Relating to Certain Financial Instruments

The Fund may invest in mortgage securities, including securities issued by Federal National Mortgage Association (“FNMA”) and Federal Home Loan Mortgage Corporation (“FHLMC”). These are fixed income securities that derive their value from or represent interests in a pool of mortgages or mortgage securities. An unexpectedly high rate of defaults on the mortgages held by a mortgage pool may adversely affect the value of a mortgage backed security and could result in losses to the Fund. The risk of such defaults is

25

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

generally higher in the case of mortgage pools that include sub-prime mortgages. Sub-prime mortgages refer to loans made to borrowers with weakened credit histories or with a lower capacity to make timely payments on their mortgages. The securities held by the Fund are not backed by sub-prime mortgages.

Additionally, securities issued by FNMA and FHLMC are not backed by or entitled to the full faith and credit of the United States; rather, they are supported by the right of the issuer to borrow from the U.S. Department of the Treasury.

The Federal Housing Finance Agency (“FHFA”) serves as conservator of FNMA and FHLMC and the U.S. Department of the Treasury has agreed to provide capital as needed to ensure FNMA and FHLMC continue to provide liquidity to the housing and mortgage markets.

8. Shares of Beneficial Interest

Transactions in shares of beneficial interest were as follows:

	FOR THE SIX MONTHS ENDED NOVEMBER 30, 2012						FOR THE YEAR ENDED MAY 31, 2012
	(unaudited)
	SHARES			AMOUNT			SHARES			AMOUNT
Shares sold		6,424,842		$	59,882,840			9,381,448		$	87,734,716
Reinvestment of dividends		169,825			1,582,167			390,412			3,627,398
		6,594,667			61,465,007			9,771,860			91,362,114
Shares redeemed		(4,770,057	)		(44,432,969	)		(11,019,187	)		(103,020,467	)
Net increase (decrease)		1,824,610		$	17,032,038			(1,247,327	)	$	(11,658,353	)

9. Federal Income Tax Status

It is the Fund’s intention to continue to qualify as a regulated investment company and distribute all of its taxable and tax-exempt income. Accordingly, no provision for Federal income taxes is required in the financial statements.

Dividend income and distributions to shareholders are recorded on the ex-dividend date. Interest income is recognized on an accrual basis. Dividends from net investment income, if any, are declared daily and paid monthly. Net realized capital gains, if any, are distributed at least annually.

The Fund may be subject to taxes imposed by countries in which it invests. Such taxes are generally based on income and/or capital gains earned or repatriated. Taxes are accrued based on net investment income, net realized gains and net unrealized appreciation as such income and/or gains are earned. Taxes may also be based on transactions in foreign currency and are accrued based on the value of investments denominated in such currency.

26

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

FASB ASC 740-10, Income Taxes — Overall, sets forth a minimum threshold for financial statement recognition of the benefit of a tax position taken or expected to be taken in a tax return. Management has concluded there are no significant uncertain tax positions that would require recognition in the financial statements. If applicable, the Fund recognizes interest accrued related to unrecognized tax benefits in “Interest expense” and penalties in “Other expenses” in the Statement of Operations. The Fund files tax returns with the U.S. Internal Revenue Service, New York and various states. Each of the tax years in the four-year period ended May 31, 2012, remains subject to examination by taxing authorities.

The tax character of distributions paid may differ from the character of distributions shown in the Statements of Changes in Net Assets due to short-term capital gains being treated as ordinary income for tax purposes. The tax character of distributions paid during fiscal 2012 and 2011 was as follows:

2012 DISTRIBUTIONS PAID FROM: ORDINARY INCOME	2011 DISTRIBUTIONS PAID FROM: ORDINARY INCOME
$3,627,398	$4,733,810

The amount and character of income and gains to be distributed are determined in accordance with income tax regulations which may differ from GAAP. These book/tax differences are either considered temporary or permanent in nature.

Temporary differences are primarily due to differing book and tax treatments in the timing of the recognition of gains (losses) on certain investment transactions and the timing of the deductibility of certain expenses.

Permanent differences, primarily due to losses on paydowns and tax adjustments on swaps and debt securities sold by the Fund, resulted in the following reclassifications among the Fund’s components of net assets at May 31, 2012:

ACCUMULATED UNDISTRIBUTED NET INVESTMENT INCOME	ACCUMULATED NET REALIZED LOSS	PAID-IN-CAPITAL
$1,654,789	$(1,654,789)	—

At May 31, 2012, the components of distributable earnings for the Fund on a tax basis were as follows:

UNDISTRIBUTED ORDINARY INCOME	UNDISTRIBUTED LONG-TERM CAPITAL GAINS
$97,431	—

At November 30, 2012, the aggregate cost for federal income tax purposes approximates the aggregate cost for book purposes. The aggregate gross unrealized appreciation is $3,055,484 and the aggregate gross unrealized depreciation is $924,314 resulting in net unrealized appreciation of $2,131,170.

27

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

On December 22, 2010, the Regulated Investment Company Modernization Act of 2010 (the “Modernization Act”) was signed into law. The Modernization Act modernizes several tax provisions related to Regulated Investment Companies (“RICs”) and their shareholders. One key change made by the Modernization Act is that capital losses will generally retain their character as short-term or long-term and may be carried forward indefinitely to offset future gains. These losses are utilized before other capital loss carryforwards that expire. Generally, the Modernization Act is effective for taxable years beginning after December 22, 2010.

At May 31, 2012, the Fund had available for Federal income tax purposes capital loss carryforwards which will expire on the indicated dates:

AMOUNT		EXPIRATION
$	19,634,390	May 31, 2013
	41,142,206	May 31, 2014
	11,216,366	May 31, 2015
	5,062,831	May 31, 2018
	535,938	May 31, 2019

To the extent that capital loss carryforwards are used to offset any future capital gains realized during the carryover period as provided by U.S. Federal income tax regulations, no capital gains tax liability will be incurred by a Fund for gains realized and not distributed. To the extent that capital gains are offset, such gains will not be distributed to the shareholders. During the year ended May 31, 2012, the Fund utilized capital loss carryforwards for U.S. Federal income tax purposes of $818,923.

Capital losses and specified ordinary losses, including currency losses, incurred after October 31 but within the taxable year are deemed to arise on the first day of the Fund’s next taxable year. For the year ended May 31, 2012, the Fund deferred to June 1, 2012 for U.S. Federal income tax purposes the following losses:

POST-OCTOBER CURRENCY AND SPECIFIED ORDINARY LOSSES	POST-OCTOBER CAPITAL LOSSES
—	$708,842

10. Expense Offset

The Fund has entered into an arrangement with State Street (the “Custodian”), whereby credits realized on uninvested cash balances may be used to offset a portion of the Fund’s expenses. If applicable, these custodian credits are shown as “Expense offset” in the Statement of Operations.

11. Accounting Pronouncement

In December 2011, FASB issued Accounting Standards Update (“ASU”) 2011-11, Balance Sheet: Disclosures about Offsetting Assets and Liabilities. The pronouncement improves disclosures for recognized financial and derivative instruments that are either offset on the balance sheet in accordance with the offsetting

28

Morgan Stanley Limited Duration U.S. Government Trust

Notes to Financial Statements ⁿ November 30, 2012  (unaudited)  continued

guidance in ASC 210-20-45, Balance Sheet: Offsetting — Other Presentation Matters or ASC 815-10-45, Derivatives: Overall — Other Presentation Matters or are subject to enforceable master netting agreements or similar agreements. The Fund will be required to disclose information about rights to offset and related arrangements (such as collateral agreements) in order to enable financial statement users to understand the effect of those rights and arrangements on its financial position as well as disclose the following (1) gross amounts; (2) amounts offset in the statement of financial position; (3) any other amounts that can be offset in the event of bankruptcy, insolvency or default of any of the parties (including cash and noncash financial collateral); and (4) the Fund’s net exposure. The requirements are effective for annual reporting periods beginning on or after January 1, 2013, and must be applied retrospectively. At this time, the Fund’s management is evaluating the implications of ASU 2011-11 and its impact, if any, on the financial statements.

29

Morgan Stanley Limited Duration U.S. Government Trust

Financial Highlights

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

	FOR THE SIX MONTHS ENDED NOVEMBER 30, 2012			FOR THE YEAR ENDED MAY 31,
				2012			2011			2010^			2009^			2008^
	(unaudited)
Selected Per Share Data:
Net asset value, beginning of period		$9.33			$9.36			$9.36			$9.33			$9.25			$9.00
Income from investment operations:
Net investment income		0.03			0.09			0.09			0.10			0.23			0.36
Net realized and unrealized gain		0.00	(1)		0.04			0.07			0.08			0.13			0.25
Total income from investment operations		0.03			0.13			0.16			0.18			0.36			0.61
Less dividends from net investment income		(0.07	)		(0.16	)		(0.16	)		(0.15	)		(0.28	)		(0.36	)
Net asset value, end of period		$9.29			$9.33			$9.36			$9.36			$9.33			$9.25
Total Return(2)		0.32	%(5)		1.44	%		1.75	%		2.00	%		3.93	%		6.87	%
Ratios to Average Net Assets:
Net expenses		0.71	%(3)(6)		0.74	%(3)		0.71	%(3)		0.70	%(3)		0.76	%(3)		0.78	%(3)
Net investment income		0.56	%(3)(6)		0.97	%(3)		1.15	%(3)		1.21	%(3)		2.72	%(3)		3.88	%(3)
Rebate from Morgan Stanley affiliate		0.01	%(6)		0.01	%		0.00	%(4)		0.01	%		0.03	%		0.00	%(4)
Supplemental Data:
Net assets, end of period, in thousands		$221,141			$205,096			$217,528			$290,566			$173,826			$369,342
Portfolio turnover rate		95	%(5)		182	%		99	%		150	%		237	%		27	%

^ Beginning with the year ended May 31, 2011, the Fund was audited by Ernst & Young LLP. The previous years were audited by another independent registered public accounting firm.

(1) Amount is less than $0.005.

(2) Calculated based on the net asset value as of the last business day of the period.

(3) The ratios reflect the rebate of certain Fund expenses in connection with investments in a Morgan Stanley affiliate during the period. The effect of the rebate on the ratios is disclosed in the above table as “Rebate from Morgan Stanley affiliate.”

(4) Amount is less than 0.005%.

(5) Not annualized.

(6) Annualized.

See Notes to Financial Statements

30

Morgan Stanley Limited Duration U.S. Government Trust

U.S. Privacy Policy (unaudited)

An Important Notice Concerning Our U.S. Privacy Policy

This privacy notice describes the U.S. privacy policy of Morgan Stanley Distribution, Inc., and the Morgan Stanley family of mutual funds (“us”, “our”, “we”).

We are required by federal law to provide you with notice of our U.S. privacy policy (“Policy”). This Policy applies to both our current and former clients unless we state otherwise and is intended for individual clients who purchase products or receive services from us for personal, family or household purposes. This Policy is not applicable to partnerships, corporations, trusts or other non-individual clients or account holders, nor is this Policy applicable to individuals who are either beneficiaries of a trust for which we serve as trustee or participants in an employee benefit plan administered or advised by us. This Policy is, however, applicable to individuals who select us to be a custodian of securities or assets in individual retirement accounts, 401(k) accounts, or accounts subject to the Uniform Gifts to Minors Act.

This notice sets out our business practices to protect your privacy; how we collect and share personal information about you; and how you can limit our sharing or certain uses by others of this information. We may amend this Policy at any time, and will inform you of any changes to our Policy as required by law.

We Respect Your Privacy

We appreciate that you have provided us with your personal financial information and understand your concerns about your information. We strive to safeguard the information our clients entrust to us. Protecting the confidentiality and security of client information is an important part of how we conduct our business.

This notice describes what personal information we collect about you, how we collect it, when we may share it with others, and how certain others may use it. It discusses the steps you may take to limit our sharing of certain information about you with our affiliated companies, including, but not limited to our affiliated banking businesses, brokerage firms and credit service affiliates. It also discloses how you may limit our affiliates’ use of shared information for marketing purposes.

Throughout this Policy, we refer to the nonpublic information that personally identifies you as “personal information.” We also use the term “affiliated company” in this notice. An affiliated company is a company in our family of companies and includes companies with the Morgan Stanley name. These affiliated companies are financial institutions such as broker-dealers, banks, investment advisers and credit card issuers. We refer to any company that is not an affiliated company as a nonaffiliated third party. For purposes of Section 5 of this notice, and your ability to limit certain uses of personal information by our affiliates, this notice applies to the use of personal information by our affiliated companies.

31

Morgan Stanley Limited Duration U.S. Government Trust

U.S. Privacy Policy (unaudited)  continued

1.  What Personal Information Do We Collect From You?

We may collect the following types of information about you: (i) information provided by you, including information from applications and other forms we receive from you, (ii) information about your transactions with us or our affiliates, (iii) information about your transactions with nonaffiliated third parties, (iv) information from consumer reporting agencies, (v) information obtained from our websites, and (vi) information obtained from other sources. For example:

• We collect information such as your name, address, e-mail address, telephone/fax numbers, assets, income and investment objectives through applications and other forms you submit to us.

• We may obtain information about account balances, your use of account(s) and the types of products and services you prefer to receive from us through your dealings and transactions with us and other sources.

• We may obtain information about your creditworthiness and credit history from consumer reporting agencies.

• We may collect background information from and through third-party vendors to verify representations you have made and to comply with various regulatory requirements.

2.  When Do We Disclose Personal Information We Collect About You?

We may disclose personal information we collect about you in each of the categories listed above to affiliated and nonaffiliated third parties.

a. Information We Disclose to Affiliated Companies.    We may disclose personal information that we collect about you to our affiliated companies to manage your account(s) effectively, to service and process your transactions, and to let you know about products and services offered by us and affiliated companies, to manage our business, and as otherwise required or permitted by law. Offers for products and services from affiliated companies are developed under conditions designed to safeguard your personal information.

b. Information We Disclose to Third Parties.    We may disclose personal information that we collect about you to nonaffiliated third parties to provide marketing services on our behalf or to other financial institutions with whom we have joint marketing agreements. We may also disclose all of the information we collect to other nonaffiliated third parties for our everyday business purposes, such as to process transactions, maintain account(s), respond to court orders and legal investigations, report to credit bureaus, offer our own products and services, protect against fraud, for institutional risk control, to perform services on our behalf, and as otherwise required or permitted by law.

When we share personal information about you with a nonaffiliated third party, they are required to limit their use of personal information about you to the particular purpose for which it was shared and they are not allowed to share personal information about you with others except to fulfill that limited purpose or as may be permitted or required by law.

32

Morgan Stanley Limited Duration U.S. Government Trust

U.S. Privacy Policy (unaudited)  continued

3.  How Do We Protect The Security and Confidentiality Of Personal Information We Collect About You?

We maintain physical, electronic and procedural security measures that comply with applicable law and regulations to help safeguard the personal information we collect about you. We have internal policies governing the proper handling of client information by employees. Third parties that provide support or marketing services on our behalf may also receive personal information about you, and we require them to adhere to appropriate security standards with respect to such information.

4.  How Can You Limit Our Sharing Certain Personal Information About You With Our Affiliated Companies For Eligibility Determination?

By following the opt-out procedures in Section 6 below, you may limit the extent to which we share with our affiliated companies, personal information that was collected to determine your eligibility for products and services such as your credit reports and other information that you have provided to us or that we may obtain from third parties (“eligibility information”). Eligibility information does not include your identification information or personal information pertaining to our transactions or experiences with you. Please note that, even if you direct us not to share eligibility information with our affiliated companies, we may still share your personal information, including eligibility information, with our affiliated companies under circumstances that are permitted under applicable law, such as to process transactions or to service your account.

5.  How Can You Limit the Use of Certain Personal Information About You by Our Affiliated Companies for Marketing?

By following the opt-out instructions in Section 6 below, you may limit our affiliated companies from marketing their products or services to you based on personal information we disclose to them. This information may include, for example, your income and account history with us. Please note that, even if you choose to limit our affiliated companies from using personal information about you that we may share with them for marketing their products and services to you, our affiliated companies may use your personal information that they obtain from us to market to you in circumstances permitted by law, such as if the affiliated party has its own relationship with you.

6.  How Can You Send Us an Opt-Out Instruction?

If you wish to limit our sharing of eligibility information about you with our affiliated companies, or our affiliated companies’ use of personal information for marketing purposes, as described in this notice, you may do so by:

• Calling us at (800) 548-7786

Monday-Friday between 8a.m. and 5p.m. (EST)

33

Morgan Stanley Limited Duration U.S. Government Trust

U.S. Privacy Policy (unaudited)  continued

• Writing to us at the following address:

Morgan Stanley Services Company Inc.

c/o Privacy Coordinator

201 Plaza Two, 3rd Floor

Jersey City, New Jersey 07311

If you choose to write to us, your request should include: your name, address, telephone number and account number(s) to which the opt-out applies and whether you are opting out with respect to sharing of eligibility information (Section 4 above), or information used for marketing (Section 5 above), or both. Written opt-out requests should not be sent with any other correspondence. In order to process your request, we require that the request be provided by you directly and not through a third party. Once you have informed us about your privacy preferences, your opt-out preference will remain in effect with respect to this Policy (as it may be amended) until you notify us otherwise. If you are a joint account owner, we will accept instructions from any one of you and apply those instructions to the entire account.

Please understand that if you limit our sharing or our affiliated companies’ use of personal information, you and any joint account holder(s) may not receive information about our affiliated companies’ products and services, including products or services that could help you manage your financial resources and achieve your investment objectives.

If you have more than one account or relationship with us, please specify the accounts to which you would like us to apply your privacy choices. If you have accounts or relationships with our affiliates, you may receive multiple privacy policies from them, and will need to separately notify those companies of your privacy choices for those accounts or relationships.

7.  What if an affiliated company becomes a nonaffiliated third party?

If, at any time in the future, an affiliated company becomes a nonaffiliated third party, further disclosures of personal information made to the former affiliated company will be limited to those described in Section 2(b) above relating to nonaffiliated third parties. If you elected under Section 6 to limit disclosures we make to affiliated companies, or use of personal information by affiliated companies, your election will not apply to use by any former affiliated company of your personal information in their possession once it becomes a nonaffiliated third party.

34

Morgan Stanley Limited Duration U.S. Government Trust

U.S. Privacy Policy (unaudited)  continued

Special Notice To Residents Of Vermont

The following section supplements our Policy with respect to our individual clients who have a Vermont address and supersedes anything to the contrary in the above Policy with respect to those clients only.

The State of Vermont requires financial institutions to obtain your consent prior to sharing personal information that they collect about you with nonaffiliated third parties, or eligibility information with affiliated companies, other than in certain limited circumstances. Except as permitted by law, we will not share personal information we collect about you with nonaffiliated third parties or eligibility information with affiliated companies, unless you provide us with your written consent to share such information.

Special Notice To Residents Of California

The following section supplements our Policy with respect to our individual clients who have a California address and supersedes anything to the contrary in the above Policy with respect to those clients only.

In response to a California law, if your account has a California home address, your personal information will not be disclosed to nonaffiliated third parties except as permitted by applicable California law, and we will limit sharing such personal information with our affiliates to comply with California privacy laws that apply to us.

35

Item 2. Code of Ethics.

Not applicable for semiannual reports.

Item 3. Audit Committee Financial Expert.

Not applicable for semiannual reports.

Item 4. Principal Accountant Fees and Services

Not applicable for semiannual reports.

Item 5. Audit Committee of Listed Registrants.

Not applicable for semiannual reports.

Item 6.

(a) Refer to Item 1.

(b) Not applicable.

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End Management Investment Companies.

Not applicable for semiannual reports.

Item 8. Portfolio Managers of Closed-End Management Investment Companies

Applicable only to annual reports filed by closed-end funds.

Item 9. Closed-End Fund Repurchases

Applicable to reports filed by closed-end funds.

Item 10. Submission of Matters to a Vote of Security Holders

Not applicable.

Item 11. Controls and Procedures

(a) The Fund’s principal executive officer and principal financial officer have concluded that the Fund’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the Fund in this Form N-CSR was recorded, processed, summarized and reported within the time periods specified in the Securities and Exchange Commission’s rules and forms, based upon such officers’ evaluation of these controls and procedures as of a date within 90 days of the filing date of the report.

(b) There were no changes in the registrant’s internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting.

Item 12. Exhibits

(a) Code of Ethics – Not applicable for semiannual reports.

(b) A separate certification for each principal executive officer and principal financial officer of the registrant are attached hereto as part of EX-99.CERT.

2

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.

Morgan Stanley Limited Duration U.S. Government Trust

/s/ Arthur Lev

Arthur Lev

Principal Executive Officer

January 22, 2013

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

/s/ Arthur Lev

Arthur Lev

Principal Executive Officer

January 22, 2013

/s/ Francis Smith

Francis Smith

Principal Financial Officer

January 22, 2013

3