<?xml version="1.0"?>

<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2003-12-31</periodOfReport>


    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000009521</issuerCik>
        <issuerName>BANCROFT CONVERTIBLE FUND INC</issuerName>
        <issuerTradingSymbol>BCV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001041813</rptOwnerCik>
            <rptOwnerName>AHALT GORDON F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>65 MADISON AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 550</rptOwnerStreet2>
            <rptOwnerCity>MORRISTOWN</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07960</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>

        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2003-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>33</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.82</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1200</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>

        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2003-12-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>16</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.82</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>600</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>

    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These shares were acquired in the Fund's 2003 Rights Offering pursuant to the Over-Subscription Privilege.  Only shareholders who subscribed for all shares allocated to them in the Primary Subscription were able to participate in the Over-Subscription Privilege.  The 2003 Rights Offering was approved by the Fund's Board of Directors.</footnote>
        <footnote id="F2">Based on the subscription price per share of 95% of the average of the volume-weighted average sales prices of a share of the BCV's Common Stock on the American Stock Exchange (&quot;AMEX&quot;) on December 17, 2003 and the four preceding trading days.</footnote>
        <footnote id="F3">The reporting person disclaims beneficial ownership of these securities, and this report shall not be deemed an admission that the reporting person is the beneficial owner of the securities for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>


    <ownerSignature>
        <signatureName>/s/ Gary I. Levine, attorney-in-fact</signatureName>
        <signatureDate>2004-01-02</signatureDate>
    </ownerSignature>

</ownershipDocument>

