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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-10-19</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001195933</issuerCik>
        <issuerName>INFINITY PROPERTY &amp; CASUALTY CORP</issuerName>
        <issuerTradingSymbol>IPCC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001557065</rptOwnerCik>
            <rptOwnerName>Bateman Robert H.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3700 COLONNADE PARKWAY, SUITE 600</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BIRMINGHAM</rptOwnerCity>
            <rptOwnerState>AL</rptOwnerState>
            <rptOwnerZipCode>35243</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Executive Vice President, CFO, and Treasurer

Exhibit List.  Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ James H. Romaker</signatureName>
        <signatureDate>2015-10-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
