The research on gearbox fault diagnosis has been gaining increasing attention in recent years, especially on single fault diagnosis. In engineering practices, there is always more than one fault in the gearbox, which is demonstrated as compound fault. Hence, it is equally important for gearbox compound fault diagnosis. Both bearing and gear faults in the gearbox tend to result in different kinds of transient impulse responses in the captured signal and thus it is necessary to propose a potential approach for compound fault diagnosis. Sparse representation is one of the effective methods for feature extraction from strong background noise. Therefore, sparse representation under wavelet bases for compound fault features extraction is developed in this paper. With the proposed method, the different transient features of both bearing and gear can be separated and extracted. Both the simulated study and the practical application in the gearbox with compound fault verify the effectiveness of the proposed method.