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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-03-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001357874</issuerCik>
        <issuerName>PRECISION BIOSCIENCES INC</issuerName>
        <issuerTradingSymbol>DTIL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001397607</rptOwnerCik>
            <rptOwnerName>Schinazi Raymond F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRECISION BIOSCIENCES, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>302 E. PETTIGREW STREET, SUITE A-100</rptOwnerStreet2>
            <rptOwnerCity>DURHAM</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>27701</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>16.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>34544</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-03-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>34544</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34544</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Convertible Promissory Note</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>13.60</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-03-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionTotalValue>
                    <value>502466.00</value>
                </transactionTotalValue>
                <transactionPricePerShare>
                    <value>500000.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>36946</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <valueOwnedFollowingTransaction>
                    <value>502466.00</value>
                </valueOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By RFS Partners, LP</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option vests as to 34% of the underlying shares on March 27, 2020 and vests in equal installments at the end of each successive three-month period over the following 24 months.</footnote>
        <footnote id="F2">On March 1, 2019, RFS Partners LP (&quot;RFS&quot;) acquired a convertible promissory note in the principal amount of $500,000 (the &quot;2019 Note&quot;) from Precision BioSciences, Inc. (the &quot;Issuer&quot;).  In connection with the pricing of the Issuer's initial public offering on March 27, 2019 (the &quot;IPO&quot;), the conversion price of the 2019 Note became fixed at 85% of the price per share in the IPO, and the 2019 Note became automatically convertible into shares of the Issuer's common stock at the closing of the IPO.</footnote>
        <footnote id="F3">The 2019 Note is held of record by RFS. RFS &amp; Associates, LLC (&quot;RFS &amp; Associates&quot;) is the general partner of RFS, and the reporting person is a limited partner of RFS as well as the manager of RFS &amp; Associates. The reporting person disclaims beneficial ownership of the 2019 Note, except to the extent of any pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Abid Ansari, Attorney-in-Fact for Raymond F. Schinazi</signatureName>
        <signatureDate>2019-03-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
