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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-12-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001587221</issuerCik>
        <issuerName>Zosano Pharma Corp</issuerName>
        <issuerTradingSymbol>ZSAN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001652910</rptOwnerCik>
            <rptOwnerName>Aisling Capital IV, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE, 12TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001737020</rptOwnerCik>
            <rptOwnerName>Aisling Capital Partners IV, LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVE., 12TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001737019</rptOwnerCik>
            <rptOwnerName>Aisling Capital Partners IV LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVE., 12TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001250195</rptOwnerCik>
            <rptOwnerName>ELMS STEVE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AISLING CAPITAL MANAGEMENT LP</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVE., 12TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001172252</rptOwnerCik>
            <rptOwnerName>SCHIFF ANDREW N</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AISLING CAPITAL MANAGEMENT LP</rptOwnerStreet1>
            <rptOwnerStreet2>888 SEVENTH AVE., 12TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10106</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value of $0.0001</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>689655</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.45</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2718226</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The securities are directly held by Aisling Capital IV, LP (&quot;Aisling&quot;), and may be deemed to be beneficially owned by Aisling Capital Partners IV, LP (&quot;Aisling GP&quot;), as general partner of Aisling, Aisling Capital Partners IV LLC (&quot;Aisling Partners&quot;), as general partner of Aisling GP, and each of the individual managing members and partners (collectively, the &quot;Managers&quot;) of Aisling GP and Aisling Partners. The Managers of Aisling Partners are Dr. Andrew Schiff and Steve Elms.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>AISLING CAPITAL IV, LP, by Aisling Capital Partners IV, LP, its General Partner, by Aisling Capital Partners IV LLC, its General Partner, /s/ Andrew Schiff, Managing Member</signatureName>
        <signatureDate>2019-12-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>AISLING CAPITAL PARTNERS IV, LP, by Aisling Capital Partners IV LLC, its General Partner, /s/ Andrew Schiff, Managing Member</signatureName>
        <signatureDate>2019-12-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>AISLING CAPITAL PARTNERS IV LLC, /s/ Andrew Schiff, Managing Member</signatureName>
        <signatureDate>2019-12-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Steve Elms</signatureName>
        <signatureDate>2019-12-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Andrew Schiff</signatureName>
        <signatureDate>2019-12-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
