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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-02-03</periodOfReport>

    <notSubjectToSection16>true</notSubjectToSection16>

    <issuer>
        <issuerCik>0001592480</issuerCik>
        <issuerName>Continental Building Products, Inc.</issuerName>
        <issuerTradingSymbol>CBPX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001598315</rptOwnerCik>
            <rptOwnerName>Power Timothy</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>12950 WORLDGATE DRIVE, SUITE 700</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HERNDON</rptOwnerCity>
            <rptOwnerState>VA</rptOwnerState>
            <rptOwnerZipCode>20170</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isOfficer>true</isOfficer>
            <officerTitle>Senior VP, GC, and Secretary</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>66676</value>
                </transactionShares>
                <transactionPricePerShare>
                    <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>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>14</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-02-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-02-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of pursuant to the Agreement and Plan of Merger by and among the Issuer, CertainTeed Gypsum and Ceilings USA, Inc., Cupertino Merger Sub, Inc. and Compagnie de Saint-Gobain S.A., in exchange for cash consideration of $37.00 per share of common stock of the Issuer (the &quot;Merger Consideration&quot;) on the effective date of the merger.</footnote>
        <footnote id="F2">This option, which provided for vesting in four equal annual installments beginning February 4, 2015, was canceled in the merger in exchange for a cash payment of $172,500 representing the difference between the exercise price of the option and the Merger Consideration ($37 per share).</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Timothy Power</signatureName>
        <signatureDate>2020-02-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
