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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-07-22</periodOfReport>

    <issuer>
        <issuerCik>0000091440</issuerCik>
        <issuerName>SNAP-ON Inc</issuerName>
        <issuerTradingSymbol>SNA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001169366</rptOwnerCik>
            <rptOwnerName>RENSI EDWARD H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>SNAP-ON INCORPORATED</rptOwnerStreet1>
            <rptOwnerStreet2>2801 80TH STREET</rptOwnerStreet2>
            <rptOwnerCity>KENOSHA</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>53143</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-07-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1990</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>96.0717</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7432.2078</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9607</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9607</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was executed in multiple trades at prices ranging from $96.03 to $96.11. The price reported above reflects the weighted average sale price. The reporting person hereby undertakes to provide upon request to the SEC staff, the Issuer or a security holder of the Issuer full information regarding the number of shares and prices at which the transaction was effectuated.</footnote>
        <footnote id="F2">Includes 87.11 shares acquired under a dividend reinvestment and direct stock purchase plan.</footnote>
        <footnote id="F3">1 for 1.</footnote>
        <footnote id="F4">All restrictions lapse upon the earliest of retirement from the Board, death or a change in control; the reporting person will receive the underlying shares upon the earliest of the reporting person's 70th birthday (in which case he will receive them in two or five equal annual installments depending on the applicable deferral election), death or a change in control.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Ryan S. Lovitz under Power of Attorney for Edward H. Rensi</signatureName>
        <signatureDate>2013-07-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
