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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-01-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000075208</issuerCik>
        <issuerName>OVERSEAS SHIPHOLDING GROUP INC</issuerName>
        <issuerTradingSymbol>OSG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001239741</rptOwnerCik>
            <rptOwnerName>JOHNSTON ROBERT E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO HARBOUR PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>302 KNIGHTS RUN AVENUE, SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>TAMPA</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33602</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; Head of US Flag Bus.Unit</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $1.00 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2012-01-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>301</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.61</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21303</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $1.00 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>60</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>(3)</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $1.00 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4821</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>(4)</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">In accordance with the terms of the Overseas Shipholding Group, Inc. 2004 Stock Incentive Plan, these 301 shares of common stock were surrendered to Overseas Shipholding Group, Inc. upon the January 10, 2012 vesting of 982 shares (the &quot;Vested Shares&quot;) of the reporting person's restricted stock in payment of the reporting person's tax withholding liability incurred as a result of the vesting of the Vested Shares.</footnote>
        <footnote id="F2">Of these 21,303 shares of common stock, 4,971 shares are subject to vesting restrictions as of January 12, 2012.</footnote>
        <footnote id="F3">The 60 shares are held in an individual retirement account (&quot;IRA&quot;).  The reporting person is a co-trustee of the IRA and has a 50% interest in the assets of the IRA, including the 60 shares.</footnote>
        <footnote id="F4">The reporting person indirectly owns these 4,821 shares of common stock through the Overseas Shipholding Group, Inc. 2000 Employee Stock Purchase Plan as of December 31, 2011.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/James I. Edelson, Attorney-in-Fact, pursuant to power of attorney previously filed</signatureName>
        <signatureDate>2012-01-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
