The　bearing　fault,　generating　harmful　vibrations,　is　one　of　the　main　causes　of　machine　breakdowns.　Therefore,　performing　bearing　fault　diagnosis　is　a　key　point　to　improve　the　reliability　of　the　mechanical　systems　and　reduce　the　corresponding　operating　expense.　Recently,　more　and　more　studies　focus　on　addressing　this　problem　through　detection　transient　signal　by　means　of　sparse　representation　(SR)　theory.　Although　tremendous　progress　has　been　made,　one　important　drawback　remains　to　be　solved:　in　the　early　stage　of　bearing　failure,　the　incipient　impact　signal　is　relatively　weak,　which　is　hard　to　detect　due　to　other　mechanical　components　harmonic　signals　and　interference　of　noise.　In　order　to　solve　this　problem,　spectral　kurtosis　(SK),　a　popular　tool　to　detect　non-stationary　signal,　is　introduced　as　a　pre-procedure　of　the　transient　signal　sparse　representation.　A　novel　sparse　representation　based　on　spectral　kurtosis　method　is　proposed　in　this　work,　namely　the　SKSR.　SKSR　utilizes　the　advantages　of　both　of　the　methods:　it　is　possible　to　choose　the　best　matching　of　the　atomic　signal　with　the　failure　signal　structure　feature　to　gain　sparse　representation　and　efficiently　extract　transient　signal　from　strong　noise.　The　effectiveness　of　the　proposed　method　is　verified　by　the　numerically　simulations　and　lab　experiments.　The　results　show　that　the　presented　method　is　efficient　for　the　title　problem.