Singular value decomposition (SVD) methods have aroused wide concern to extract the periodic impulses for bearing fault diagnosis. The state-of-the-art SVD methods mainly focus on the low rank property of the Hankel matrix for the fault feature, which cannot achieve satisfied performance when the background noise is strong. Different to the existing low rank-based approaches, we proposed a simultaneously low rank and group sparse decomposition (SLRGSD) method for bearing fault diagnosis. The major contribution is that the simultaneously low rank and group sparse (SLRGS) property of the Hankel matrix for fault feature is first revealed to improve performance of the proposed method. Firstly, we exploit the SLRGS property of the Hankel matrix for the fault feature. On this basis, a regularization model is formulated to construct the new diagnostic framework. Furthermore, the incremental proximal algorithm is adopted to achieve a stationary solution. Finally, the effectiveness of the SLRGSD method for enhancing the fault feature are profoundly validated by the numerical analysis, the artificial bearing fault experiment and the wind turbine bearing fault experiment. Simulation and experimental results indicate that the SLRGSD method can obtain superior results of extracting the incipient fault feature in both performance and visual quality as compared with the state-of-the-art methods.