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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-10-12</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001886388</rptOwnerCik>
            <rptOwnerName>Borgman Anne Elizabeth</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 October 12, 2022, the date on which Dr. Borgman joined the Curis, Inc. Board of Directors, Dr. Borgman 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/ Diantha Duvall, Attorney-in-fact</signatureName>
        <signatureDate>2022-10-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
