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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-24</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001585223</rptOwnerCik>
            <rptOwnerName>Duchemin Jeffrey</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HARVARD BIOSCIENCE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>84 OCTOBER HILL ROAD</rptOwnerStreet2>
            <rptOwnerCity>HOLLISTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01746</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1111</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.31</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>746667</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The shares were disposed of to satisfy the Reporting Person's tax withholding obligation in connection with the vesting of certain restricted stock units previously granted to the Reporting Person on May 24, 2018.</footnote>
        <footnote id="F2">Includes (a) a deferred stock award of 56,517 restricted stock units with performance based vesting conditions, which shall vest in three equal installments on March 7, 2020, 2021 and 2022, contingent upon achievement of a performance condition tied to relative total shareholder return; (b) a deferred stock award of 113,034 restricted stock units which shall vest in four equal installments on January 1, 2020, 2021, 2022 and 2023; (c) a deferred stock award of 70,833 restricted stock units which vest in equal installments on January 1, 2020, 2021 and 2022; (d) a deferred stock award of 178,804 restricted stock units which shall vest in equal installments on January 1, 2020 and 2021; (e) a deferred stock award of 72,916 restricted stock units which shall vest on January 1, 2020;</footnote>
        <footnote id="F3">continuation of footnote 2 above: (f) a deferred stock award of 7,556 restricted stock units, which vest in equal installments on May 24, 2020 and May 24, 2021; and (g) 247,007 shares of common stock held by the Reporting Person.    With respect to the performance based deferred stock award received on May 24, 2018, the Reporting Person had previously included the target number of such award, being 94,444 shares, in his reported holdings, and on May 24, 2019, the actual earned award amount was determined to be 11,333.  As such, the 83,111 shares previously reported but not earned are no longer included in the securities beneficially owned.</footnote>
    </footnotes>

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

    <ownerSignature>
        <signatureName>/s/ Chad Porter, by power of attorney</signatureName>
        <signatureDate>2019-05-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
