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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-01-17</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001348649</issuerCik>
        <issuerName>CoLucid Pharmaceuticals, Inc.</issuerName>
        <issuerTradingSymbol>CLCD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000059478</rptOwnerCik>
            <rptOwnerName>LILLY ELI &amp; CO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LILLY CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INDIANAPOLIS</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46285</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001695312</rptOwnerCik>
            <rptOwnerName>ProCar Acquisition Corp</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LILLY CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INDIANAPOLIS</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46285</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common stock</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>54683</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Eli Lilly and Company directly owns 54,683 shares of CoLucid Pharmaceuticals, Inc. (the &quot;Issuer&quot;) common stock, which represents approximately 0.3% of all shares outstanding as of January 12, 2017. Each of the Reporting Persons may be deemed to have become a 10% Owner of the Issuer in connection with the entry into certain Tender and Support Agreements dated as of January 17, 2017 (the &quot;Tender Agreements&quot;), by and among the Reporting Persons and each of Novo A/S, A.M. Pappas Life Science Ventures III, L.P., PV III CEO Fund, LP, Pappas Capital, LLC and TVM Life Science Ventures VII, L.P. (each, a &quot;Stockholder&quot;), representing an aggregate of 6,694,843 shares of the Issuer's common stock beneficially owned by the Stockholders. The Tender Agreements were entered into in connection with the Agreement and Plan of Merger, dated as of January 17, 2017, by and among the Reporting Persons and the Issuer.</footnote>
        <footnote id="F2">The Reporting Persons exercise voting power in limited situations over such shares of the Issuer's common stock through the grant of an irrevocable proxy by each of the Stockholders in the Tender Agreements. The Reporting Persons have no pecuniary interest in any of such shares of the Issuer's common stock.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Derica W. Rice, Eli Lilly and Company</signatureName>
        <signatureDate>2017-01-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Darren J. Carroll, ProCar Acquisition Corporation</signatureName>
        <signatureDate>2017-01-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
