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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-07-01</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>2020-07-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>99600</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents an award of 4,000 restricted stock units that vests in two equal installments on each of September 30, 2020 and December 31, 2020. This retainer award was granted in lieu and satisfaction of the annual cash retainer compensation to be earned by the director in connection with his service as chairman of the Audit Committee of the Issuer's Board of Directors, which service commenced on June 11, 2020. The number of shares of common stock subject to such retainer award is equal to the amount of cash that would have been received had the applicable retainer all been paid in cash on a prorated basis, divided by the average daily closing market price of the Issuer's common stock for the month of April, rounded to the nearest 100 shares.</footnote>
        <footnote id="F2">Includes (a) the award described in footnote (1) above, (b) an award of 28,100 restricted stock units vesting on the earlier to occur of (i) the date of the Issuer's next Annual Meeting of Stockholders or (ii) June 18, 2021, (c) an award of 7,850 remaining unvested restricted stock units vesting in equal quarterly installments on September 30, 2020 and December 31, 2020, and (d) 59,650 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>2020-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
