Envelope demodulation method based on resonance-based sparse signal decomposition is proposed and is applied to the fault diagnosis of roller bearings. Different form the traditional signal decomposition method based on the frequency band,resonance-based sparse signal decomposition method decomposes a signal into high resonance component and low resonance component based on the Q-factor. When a damage occurs in a roller bearing,the vibration signal of a roller bearing is composed of harmonic signal with system characteristics of roller bearing,transient impulse signal with bearing fault information and noise. The harmonic signal belongs to narrowband signal and has a high Q-factor,and can be decomposed into high resonance component；while the transient impulse signal belongs to wideband signal and has a low Q-factor,and can be decomposed into low resonance component. The proposed method decomposes the vibration signal of a roller bearing into high resonance component、low resonance component and residual component using resonance-based sparse signal decomposition, and the low resonance component is analyzed by envelope demodulation method, then the fault diagnosis of a bearing is carried on according to the envelope demodulation spectrum. Simulation and application examples show that the impulse can be extracted effectively from the fault vibration signal of a bearing and the fault feature of fault bearings can be enhanced.