In order to analyze the multi-component and multi-modulation characteristics of a gearbox fault signal, an optimal wavelet demodulation method based on singular value decomposition (SVD) is proposed. In this method, Morlet wavelet transform is used as an adaptive band-pass filter to extract the impact component in the geabox vibration signal. The minimum Shannon entropy is used as the wavelet time scale resolution index to optimize the Morlet wavelet parameters. Based on SVD, the optimal wavelet coefficient is utilized to determine the parameters. The new method can extract transient information better, reduce noise, effectively extract the signal period, and assure the validity of the fault feature recognition. The experimental results show that the proposed method can more accurately and effectively extract the fault characteristic hidden in the gearbox vibration signal.