Abstract: Most rotating machinery and equipment are continuously running under complex and changeable operating conditions in actual industrial production. The running speed can be constantly changing to switch the working mode with the excessive background noise. Among them, three-phase induction motor bearings tend to suffer multiple concurrent failures and strong interference of background noise in the signal. The sparse decomposition of composite fault signals can also be doped by various fault types. The sparse characteristics of the signals cannot be fully reflected, due to the large atomic complexity and the low sparse performance. It is a high demand for the accurate diagnosis of the weak composite fault of bearings. In this study, a hybrid fault diagnosis was proposed using the non-convex fused lasso model (NCFLM). The sparse performance of non-convex total variation denoising (NCTVD) was improved to accurately identify the faults when extracting the weak compound faults of three-phase induction motor bearings. Among them, the absolute value function of the coefficient difference was used as the punishment to compress the model coefficient. The regression coefficient was then compressed toward the origin. The coefficient with the redundancy characteristics was weakened to smooth and segment the coefficient with similar characteristics. The number of atoms was reduced with less information and the complexity of the signal, in order to meet the requirements of the ideal recognition of compound faults. Firstly, the Generalized minimax concave (GMC) was introduced into the NCTVD model (arctan-NCTVD) using the arctan-NCTVD penalty factor. The GMC penalty function was derived from the generalization of the Huber function. The form of the GMC penalty function was derived by the variable scaling, whereas, the compression scaling variables were added to the unary Huber. The GMC penalty function term was added to the arctan-NCTVD model, and then expanded into the form of a fusion lasso model, in order to obtain the NCFLM. The penalty control was simultaneously carried out on the signal data atoms themselves. The sum of the absolute values was set as the differences between NCFLM and conventional non-convex penalty model. There was a decrease in the difference between adjacent atoms with the same characteristics. The sequential association of all atoms was also considered to distinguish different feature components. As such, the processed data by the fusion lasso model was sparse for the atoms and continuity differences between them. Therefore, sparse solutions were generated between atoms and continuity differences. The sparsity of the sparse coefficient and the difference was enhanced to make the model more sensitive to the complex impact components in the signal. Secondly, the model was solved using the Forward-Backward Algorithm (FBA). The ergodic method was introduced to find the optimal value of the regularization parameters λ₁ and λ₂, when the maximum correlation kurtosis was obtained. The ergodic method was used to screen the optimal regularization parameter combination with the strong convexity of the model. The improved non-convex penalty model was achieved in better sparse performance and approximation to the ideal L₀ norm. Finally, the NCFLM processing was carried out using the collected composite fault signals of motor bearings to extract the composite fault characteristics. The measured data was obtained in the variable frequency and speed regulating three-phase asynchronous motor bearings. The experimental results show that the sparse performance of NCFLM was 9.2%, 6.6%, 10%, 46.2%, and 15% higher than that of the original arctan-NCTVD model, in terms of the atomic distribution, convergence performance, reconstruction error, sparsity and degree of approximation to L₀ norm. It can also accurately diagnose the compound fault of motor bearings that is caused by the local damage of outer and inner rings, indicating the feasibility and engineering practicability of the improved model.