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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2011-02-09</periodOfReport>

    <dateOfOriginalSubmission>2011-02-09</dateOfOriginalSubmission>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001166126</issuerCik>
        <issuerName>J C PENNEY CO INC</issuerName>
        <issuerTradingSymbol>JCP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000904503</rptOwnerCik>
            <rptOwnerName>ROTH STEVEN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VORNADO REALTY TRUST</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.50 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18584010</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By VNO Fashion LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Contract</value>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2010-10-07</value>
            </exerciseDate>
            <expirationDate>
                <value>2012-10-12</value>
                <footnoteId id="F3"/>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $0.50 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4815990</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By VSPS I L.L.C.</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person's original Form 3 incorrectly included the securities underlying the Forward Transaction (as defined below) in Table I, rather than describing them separately in Table II.  This amended Form 3 correctly includes the securities underlying the Forward Transaction in Table II and does not include these securities in Table I.</footnote>
        <footnote id="F2">Mr. Roth is a trustee and the Chairman of the Board of Trustees of Vornado Realty Trust (&quot;Vornado&quot;), which is the general partner of Vornado Realty L.P. (&quot;VRLP&quot;).  VRLP is the sole member of VNO Fashion LLC and VSPS I L.L.C (&quot;VSPS&quot;).  Mr. Roth was elected to the board of directors of the Issuer on February 9, 2011.  As a trustee of Vornado, Mr. Roth may be deemed to have a pecuniary interest in certain of the shares of the Issuer beneficially owned by Vornado.  Mr. Roth disclaims any beneficial ownership of securities of the Issuer.</footnote>
        <footnote id="F3">On October 7, 2010, VSPS entered into a share forward transaction with Deutsche Bank AG, London Branch (&quot;DB&quot;) (the &quot;Forward Transaction&quot;). Currently, 4,815,900 shares of Common Stock of the Issuer are subject to this transaction. DB has agreed to sell to VSPS, for settlement no later than October 12, 2012, 4,815,900 Common Shares at a per share forward price determined based on a formula.  At any time during the term of the Forward Transaction, VSPS may accelerate settlement of the Forward Transaction, in whole or in part, upon one business days' notice to DB, and DB may accelerate settlement of the Forward Transaction, in whole or in part, upon one year's notice to VSPS.</footnote>
        <footnote id="F4">The Forward Transaction may be settled, at the election of VSPS, in cash or by delivery of Common Shares in exchange for payment by VSPS of the forward price per share.  VSPS has agreed with DB that, while the Forward Transaction is outstanding, VSPS and its affiliates will not own or otherwise have economic exposure to more than 9.95% of the Common Shares outstanding at such time.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Steven Roth</signatureName>
        <signatureDate>2012-10-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
