Accurate　identification　of　compound　fault　in　wind　turbine　gearbox　is　very　important　for　condition　monitoring　of　wind　turbine　systems.　This　paper　proposes　a　novel　compound　fault　diagnosis　method　named　FSK-MBCNN　for　wind　turbine　gearboxes.　The　proposed　method　combines　the　fast　spectral　kurtosis　(FSK)　with　a　multi-branch　convolutional　neural　network　(MBCNN).　First,　FSK　transforms　the　one　dimensional　vibration　signal　into　the　fast　kurtogram　of　a　two　dimensional　image　as　the　input　feature　map　of　the　convolutional　neural　network　model.　Second,　a　multi-branch　module　is　proposed　to　provide　suitable　network　architecture　adapting　to　different　learning　rate　and　maximum　training　epoch.　The　experiment　results　reveal　that　the　proposed　FSK-MBCNN　method　can　diagnose　compound　fault　of　wind　turbine　gearbox　with　more　than　97%　accuracy.　The　fault　identification　accuracies　of　noised　signal　and　variable　load　signal　are　close　to　90%,　proving　the　robustness　of　the　proposed　method.　Compared　with　other　three　methods,　the　proposed　method　can　recognize　9　different　statuses　of　the　wind　turbine　gearboxes　more　accurately　in　the　aforementioned　cases.　This　fascinating　discovery　indicates　that　the　proposed　FSK-MBCNN　method　can　be　applied　to　actual　condition　monitoring　of　wind　turbines　to　reduce　the　maintenance　cost　and　the　downtime.