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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-01-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001328650</issuerCik>
        <issuerName>Bronco Drilling Company, Inc.</issuerName>
        <issuerTradingSymbol>BRNC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048462</rptOwnerCik>
            <rptOwnerName>WEXFORD CAPITAL LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>411 WEST PUTNAM AVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048485</rptOwnerCik>
            <rptOwnerName>JACOBS JOSEPH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LLC</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVENUE</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001001391</rptOwnerCik>
            <rptOwnerName>DAVIDSON CHARLES E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LLC</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVENUE</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2007-01-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>108300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.0241</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4993624</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Bronco Drilling Holdings, L.L.C.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2007-01-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4893624</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Bronco Drilling Holdings, L.L.C.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2007-02-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>643830</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.1810</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4249794</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Bronco Drilling Holdings, L.L.C.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These shares of common stock are owned directly by Bronco Drilling Holdings, L.L.C. (?Bronco Holdings?). Wexford Capital LLC (?Wexford?), as manager of Bronco Holdings, may be deemed to beneficially own all the shares of common stock which are owned by Bronco Holdings. Charles E. Davidson (?Davidson?) and Joseph M. Jacobs (?Jacobs ?) are the managing members of Wexford and as such may be deemed to beneficially own all the shares of common stock which are owned by Bronco Holdings. Wexford, Davidson and Jacobs each disclaim beneficial ownership of the securities reported hereby and this report shall not be deemed as an admission that they are the beneficial owners of such securities except in the case of Davidson and Jacobs to the extent of their interests in each member of Bronco Holdings.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Arthur Amron, Partner and Secretary</signatureName>
        <signatureDate>2007-02-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Joseph M. Jacobs</signatureName>
        <signatureDate>2007-02-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Charles E. Davidson</signatureName>
        <signatureDate>2007-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
