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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001337856</rptOwnerCik>
            <rptOwnerName>BLACKLEY IAN T</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1301 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>42ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock, par value $.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>94017</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>107024</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock, par value $.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>36541</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>70483</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class B Common Stock, par value $.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3447</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-01-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>85470</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>94017</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>170940</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to buy)</value>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.20</value>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-09-29</value>
                <footnoteId id="F4"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>144382</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-09-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>144382</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>144382</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.85</value>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-02-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>683633</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-01-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                    <footnoteId id="F5"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>683633</value>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>683633</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These 94,017 shares of Class A Common Stock were acquired upon the vesting of 85,470 restricted stock units on January 20, 2016 pursuant to the Overseas Shipholding Group, Inc. (&quot;OSG&quot;) Management Incentive Compensation Plan (the &quot;Plan&quot;).  Each unit represents the right to acquire 1.1 shares of Class A Common Stock (reflecting the stock dividend of one share of Class A Common Stock for every ten shares of Class A Common Stock paid in December 2015).  The vested units were settled in shares of Class A Common Stock.  In connection with the vesting of the units, 36,541 shares of Class A Common Stock were withheld by OSG in payment of the reporting person's tax withholding liability incurred as a result of the vesting of the units.</footnote>
        <footnote id="F2">Prior to the foregoing transactions described in note (1), the reporting person reported ownership of 11,512 shares of Class A Common Stock which increased in December 2015 by the payment of the stock dividend of one share of Class A Common Stock for every ten shares of Class A Common Stock owned (1,151 shares paid to the reporting person) and one share of Class A Common Stock for every ten shares of Class B Common Stock owned (344 shares paid to the reporting person) or a total of 1,495 shares of Class A Common Stock paid to the reporting person (resulting in total ownership of 13,007 shares of Class A Common Stock).</footnote>
        <footnote id="F3">These 85,470 restricted stock units vested on January 20, 2016 and were settled in 94,017 shares of Class A Common Stock as reported in Table I on this Form 4.</footnote>
        <footnote id="F4">As previously reported, on September 29, 2014 OSG granted the reporting person pursuant to the Plan 126,582 options to purchase 126,582 shares of Class A common stock at an exercise price of $3.65 per share which became exercisable as to one third of such options on the first, second and third anniversary of the date of grant.  In December 2015, the registrant paid a stock dividend of one share of Class A common stock for every ten shares of Class A stock owned.  As a result of the stock dividend, the stock options are exercisable for 144,382 shares of Class A common stock at an exercise price of $3.20 per share.  These adjustments were made so that the value of the options before the stock dividend would be the same after the stock dividend.  The vesting schedule remains unchanged.</footnote>
        <footnote id="F5">As previously reported, on February 10, 2015 OSG granted the reporting person pursuant to the Plan 599,520 shares of Class A common stock at an exercise price of $3.25 per share which became exercisable as to one-third of such options on the first, second and third anniversary of January 20, 2015.  In December 2015, the registrant paid a stock dividend of one share of Class A common stock for every ten shares of Class A common stock owned.  As a result of the stock dividend, the stock options are exercisable for 683,633 shares of Class A common stock at an exercise price of $2.85 per share.  The adjustments were made so that the value of the options before the stock dividend would be the same after the stock dividend.  The vesting schedule remains unchanged.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/James I. Edelson, Attorney-in-Fact, pursuant to power of attorney previously filed</signatureName>
        <signatureDate>2016-02-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
