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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-01-14</periodOfReport>

    <issuer>
        <issuerCik>0000073887</issuerCik>
        <issuerName>Bristow Group Inc</issuerName>
        <issuerTradingSymbol>BRS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001505021</rptOwnerCik>
            <rptOwnerName>Allman Brian J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2103 CITY WEST BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>4TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77042</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isOfficer>1</isOfficer>
            <officerTitle>See Remarks</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-01-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2341</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>43.79</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2341</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-01-14</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2341</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>55.59</value>
                    <footnoteId id="F2"/>
                </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>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>43.79</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2013-01-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2341</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-06-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2341</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4684</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Open market sale pursuant to a 10b5-1 trading plan adopted by the Reporting Person in accordance with Rule 10b5-1 of the Securities and Exchange Act of 1934, as amended.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. The reporting person undertakes to provide to the issuer, any security holder of the issuer or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this Form 4. These shares were sold in multiple transactions on January 14, 2013 at prices ranging from $55.38 to $55.67, inclusive.</footnote>
        <footnote id="F3">Options granted on June 8, 2011 vest in three equal annual installments beginning on the first anniversary of the date of grant.</footnote>
    </footnotes>

    <remarks>Vice President, Chief Accounting Officer and Controller</remarks>

    <ownerSignature>
        <signatureName>/s/ Chip Earle, Attorney-in-Fact</signatureName>
        <signatureDate>2013-01-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
