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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000806628</issuerCik>
        <issuerName>DNP SELECT INCOME FUND INC</issuerName>
        <issuerTradingSymbol>DNP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001359933</rptOwnerCik>
            <rptOwnerName>Smith Randle L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>200 SOUTH WACKER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Officer of Adviser</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-08</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2015-12-08</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1975</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.01</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11586</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17385</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person is Randle L. Smith and he may be deemed to have a &quot;pecuniary  interest&quot; as defined in Rule 16a (a) (2) in any shares of the common stock of the issuer owned by his spouse. However, the reporting person disclaims beneficial ownership of such shares.</footnote>
        <footnote id="F2">Of these shares 1,110 were acquired through a dividend reinvestment plan meeting the requirements of Rule 16a-11 promulgated under the Securities Exchange Act of 1934.</footnote>
        <footnote id="F3">Of these shares 3,941 were acquired through a dividend reinvestment plan meeting the requirements of Rule 16a-11 promulgated under the Securities Exchange Act of 1934.</footnote>
    </footnotes>

    <remarks>See attached &quot;FOOTNOTES&quot;</remarks>

    <ownerSignature>
        <signatureName>Joyce Riegel</signatureName>
        <signatureDate>2015-12-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
