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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-11-04</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001017793</issuerCik>
        <issuerName>SUN BANCORP INC /NJ/</issuerName>
        <issuerTradingSymbol>SNBC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001026610</rptOwnerCik>
            <rptOwnerName>ROSS WILBUR L JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>319 CLEMATIS STREET, ROOM 1000</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WEST PALM BEACH</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33401</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001498175</rptOwnerCik>
            <rptOwnerName>WLR SBI AcquisitionCo, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1166 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001429295</rptOwnerCik>
            <rptOwnerName>WLR Recovery Associates IV LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1166 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431791</rptOwnerCik>
            <rptOwnerName>El Vedado, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>319 CLEMATIS STREET, ROOM 1000</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WEST PALM BEACH</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33401</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001202045</rptOwnerCik>
            <rptOwnerName>WL ROSS &amp; CO LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1166 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001414643</rptOwnerCik>
            <rptOwnerName>WLR Recovery Fund IV LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1166 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001431790</rptOwnerCik>
            <rptOwnerName>WL Ross Group, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1166 AVENUE OF THE AMERICAS</rptOwnerStreet1>
            <rptOwnerStreet2>27TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10036</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>2010-11-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10656500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12469000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Mandatorily Conv. Cum. Non-Voting Perpetual Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4</value>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-11-04</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>C</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10656500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10656500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The 12,469,000 shares of Common Stock are held directly by WLR SBI AcquisitionCo, LLC.</footnote>
        <footnote id="F2">Wilbur L. Ross, Jr. is the managing member of El Vedado, LLC, the general partner of WL Ross Group, L.P., which in turn is the managing member of WLR Recovery Associates IV LLC.  WLR Recovery Associates IV LLC is the general partner of WLR Recovery Fund IV, L.P., which is the sole manager of WLR SBI AcquisitionCo, LLC, and WL Ross &amp; Co. LLC is the investment manager of WL Ross Group, L.P.  Accordingly, WLR Recovery Fund IV, L.P., WLR Recovery Associates IV LLC, WL Ross Group, L.P., El Vedado, LLC, Wilbur L. Ross, Jr. and WL Ross &amp; Co. LLC may be deemed to share voting and dispositive power over the common stock held by WLR SBI AcquisitionCo, LLC.</footnote>
        <footnote id="F3">Shares of Mandatorily Convertible Cumulative Non-Voting Perpetual Preferred Stock,  Series B  (the &quot;Series B Preferred Stock&quot;)  converted into shares of common stock after the holders of common stock as of September 15, 2010 approved an amendment to Sun Bancorp, Inc.'s Amended and Restated Certificate of Incorporation to increase the number of authorized shares of common stock to 100,000,000 and approve the issuance of such converted shares of common stock to investors including, but not limited to, the Reporting Persons.</footnote>
        <footnote id="F4">The conversion price per share of Series B Preferred Stock was $4.00.  The number of shares of Common Stock issued upon conversion of a share of Series B Preferred Stock was determined by dividing: (i) the $1,000 liquidation preference, plus all accrued and unpaid dividends for any prior dividend periods, by (ii) the conversion price of $4.00. The shares of Series B Preferred Stock were converted into Common Stock on November 4, 2010.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Wilbur L. Ross, Jr.</signatureName>
        <signatureDate>2010-11-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
