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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2002-02-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000021178</issuerCik>
        <issuerName>PROSPECT STREET INCOME SHARES INC</issuerName>
        <issuerTradingSymbol>CNN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001365257</rptOwnerCik>
            <rptOwnerName>Deadman Davis R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>13455 NOEL ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1300</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75240</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Affiliate - Investment Advisor</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right-to-Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.75</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2002-02-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2002-02-28</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-02-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>14285.72</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Per share exercise price of each option shall be the greater of (a) the price specified in Column 2 and (b) fifty percent (50%) of the fair market value of the underlying shares of Prospect Street Income Shares, Inc. (&quot;CNN&quot;) on the date of exercise.</footnote>
        <footnote id="F2">Options to purchase shares of common stock, par value $1.00 per share, of CNN granted pursuant to the HCM Services Employee Option Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Davis R. Deadman</signatureName>
        <signatureDate>2006-06-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
