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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-24</periodOfReport>

    <issuer>
        <issuerCik>0000354190</issuerCik>
        <issuerName>GALLAGHER ARTHUR J &amp; CO</issuerName>
        <issuerTradingSymbol>AJG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001386997</rptOwnerCik>
            <rptOwnerName>Pietrucha Susan E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2850 GOLF ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ROLLING MEADOWS</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60008-4002</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isOfficer>1</isOfficer>
            <officerTitle>Chief Human Resources Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-24</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1990</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>84.29</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock (restricted)</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16975</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported is an average weighted price. The shares were sold in multiple transactions at prices ranging from $84.28 to $84.30. The reporting person will provide to the Securities and Exchange Commission staff, the issuer, or any security holder of the issuer, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
    </footnotes>

    <remarks>This transaction is being reported late because of a failure in the notification system of a third-party Section 16 filing vendor used by the Company to help it administer filings on behalf of Section 16 officers. The reporting person followed Company procedures with respect to transactions in Company stock. The Company intends to implement an additional, manual control around notifications going forward.</remarks>

    <ownerSignature>
        <signatureName>/s/ April Hanes-Dowd, by power of attorney</signatureName>
        <signatureDate>2019-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
