<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-07-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000834933</issuerCik>
        <issuerName>ACM GOVERNMENT OPPORTUNITY FUND INC</issuerName>
        <issuerTradingSymbol>ACM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000022272</rptOwnerCik>
            <rptOwnerName>COMBINED INSURANCE CO OF AMERICA</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>AON CORPORATION - CORPORATE LAW DEPT</rptOwnerStreet1>
            <rptOwnerStreet2>200 EAST RANDOLPH DRIVE, 8TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60601</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-07-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.1464</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3790236</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The designated Reporting Person is filing this Form 4 on behalf of itself and Aon Corporation (&quot;Aon&quot;) and Aon Advisors, Inc. (&quot;Advisors&quot;).</footnote>
        <footnote id="F2">Aon, Advisors and the Reporting Person share the address reported herein.  Aon's I.R.S. Identification Number is 36-3051915.  Advisors' I.R.S. Identification Number is 54-1392321.</footnote>
        <footnote id="F3">Advisors indirectly beneficially owns the securities being reported herein due to its status as investment adviser to the Reporting Person.  Aon also indirectly beneficially owns such securities due to its status as the parent corporation of both the Reporting Person and Advisors.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Jennifer L. Kraft pursuant to a power of attorney</signatureName>
        <signatureDate>2004-07-12</signatureDate>
    </ownerSignature>
</ownershipDocument>

