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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-06-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001123494</issuerCik>
        <issuerName>HARVARD BIOSCIENCE INC</issuerName>
        <issuerTradingSymbol>HBIO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001195340</rptOwnerCik>
            <rptOwnerName>EDRICK ALAN I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HARVARD BIOSCIENCE</rptOwnerStreet1>
            <rptOwnerStreet2>84 OCTOBER HILL ROAD</rptOwnerStreet2>
            <rptOwnerCity>HOLLILSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01746</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>2020-06-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>28100</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>95600</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents an award of 28,100 restricted stock units that fully vest on the earlier to occur of (i) the date of the Issuer's next Annual Meeting of Stockholders after June 11, 2020, immediately prior to the commencement of such meeting, and (ii) June 18, 2021.</footnote>
        <footnote id="F2">Includes (a) the award described in footnote (1) above, (b) a restricted stock unit award of 11,775 remaining unvested restricted stock units vesting in equal quarterly installments on June 30, 2020, September 30, 2020 and December 31, 2020, and (c) 55,725 shares of common stock held by the Reporting Person.</footnote>
    </footnotes>

    <remarks>This form has been signed under power of attorney.</remarks>

    <ownerSignature>
        <signatureName>/s/ David Sirois, by power of attorney</signatureName>
        <signatureDate>2020-06-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
