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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-05-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001361872</issuerCik>
        <issuerName>Shermen WSC Acquisition Corp</issuerName>
        <issuerTradingSymbol>SACQ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001399260</rptOwnerCik>
            <rptOwnerName>Moshenek G Kenneth</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>365 CANAL STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2900</rptOwnerStreet2>
            <rptOwnerCity>NEW ORLEANS</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>70130</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-05-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>217543</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>966117</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-05-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>829065</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>137052</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shermen WSC Holding LLC, of which the reporting person is a member, transferred to a third party the rights to receive 857,142 shares of Class A Common Stock upon their release from escrow on December 28, 2009 in exchange for the third party's agreement to purchase shares of the issuer's common stock and vote such shares in favor of the matters voted on at the issuer's annual meeting on May 26, 2009. The number of shares set forth herein reflects the proportionate interest of the reporting person in Shermen WSC Holding LLC.</footnote>
        <footnote id="F2">Shares are held directly by Shermen WSC Holding LLC, of which the reporting person is a member. The reporting person disclaims beneficial ownership of the shares except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F3">Shermen WSC Holding LLC surrendered 3,266,608 shares to the issuer for cancellation in accordance with an agreement among Shermen WSC Holding LLC, ED&amp;F Man Holdings Limited and the issuer. Shermen WSC Holding LLC and the reporting person did not receive any cash or other securities from the issuer in exchange for such shares. The number of shares set forth herein reflects the proportionate interest of the reporting person in Shermen WSC Holding LLC.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ G. Kenneth Moshenek</signatureName>
        <signatureDate>2009-06-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
