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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-03-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001244748</rptOwnerCik>
            <rptOwnerName>MCNAMARA GERALDINE M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DUFF &amp; PHELPS INVESTMENT MANAGEMENT</rptOwnerStreet1>
            <rptOwnerStreet2>200 SOUTH WACKER DRIVE, SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</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>2021-03-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4287</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14655.1822</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares were received pursuant to merger agreement between issuer and Duff &amp; Phelps Utilities and Corporate Bond Trust Inc. (DUC) in exchange for 4,062.2166 shares of DUC common stock in connection with merger of DUC into the issuer.  Shares of DUC common stock had a market value of $10.62 at the effective time of the merger</footnote>
        <footnote id="F2">This amount includes shares acquired through a dividend reinvestment plan meeting the requirements of Rule 16a-11 promulgated under the Securities Exchange Act of 1934.</footnote>
    </footnotes>

    <remarks>Exhibit List
Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ William J. Renahan, Attorney-in-fact</signatureName>
        <signatureDate>2021-03-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
