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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-12-02</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001108205</issuerCik>
        <issuerName>CURIS INC</issuerName>
        <issuerTradingSymbol>CRIS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001695378</rptOwnerCik>
            <rptOwnerName>Hohneker John</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>128 SPRING STREET</rptOwnerStreet1>
            <rptOwnerStreet2>BUILDING C - SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>LEXINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02421</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>As of December 2, 2021, the date on which Dr. Hohneker joined the Curis, Inc. Board of Directors, Dr. Hohneker did not own any securities of the Company either directly or indirectly. No securities are beneficially owned.

Exhibit Index: 24.1 Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ William Steinkrauss, Attorney-in-fact</signatureName>
        <signatureDate>2021-12-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
