As　a　new　signal　processing　method　based　on　signal　resonance　properties,　resonance-based　sparse　signal　decomposition　has　an　indetermination　in　Q-factor,　because　it　is　affected　by　the　subjectivity　of　researcher.　Fast　kurtogram　can　determine　the　bandwidth　and　central　frequency　of　filter　bank　fast　and　accurately.　Aiming　at　these,　a　fault　diagnosis　method　of　gear　based　on　the　resonance-based　sparse　decomposition　and　fast　kurtogram　is　proposed.　First,　the　bandwidth　and　central　frequency　corresponding　to　the　biggest　kurtogram　was　obtained　through　fast　kurtogram　of　gear　fault　signal,　and　the　Q-factor　can　be　counted.　Then,　the　Q-factor　is　used　in　the　resonance-based　sparse　decomposition;　therefore,　several　signal　components　in　different　frequency　bands　are　obtained.　Finally,　a　component　which　is　selected　through　central　frequency　is　demodulated　by　Hilbert　transformation　to　extract　the　fault　feature.　Result　of　engineering　signal　analysis　shows　that　the　method　can　accurately　extract　the　fault　feature　of　gear　for　diagnosis.