The over-complete dictionaries of signal sparse representation can be divided into analytical dictionary and learning dictionary according to the construction method. The analytical dictionary has a fixed structure and poor adaptability. The construction of the analytical dictionary needs to fully analyze the oscillation characteristics of the vibration signal and obtain sufficient prior knowledge. The learning dictionary gets rid of the shackles of prior knowledge and can be trained directly from the signal，with strong adaptability. Combined with the generalized minimum maximum concave penalty function，which has strong signal fidelity ability，this paper proposes a signal sparse representation method based on an adaptive learning dictionary. The proposed method improves the construction of the sample training matrix in the K-SVD algorithm，reduces the computing time，and makes up for the shortcomings of the learning dictionary's poor resistance to noise with the soft threshold algorithm. Without any prior knowledge ，the method proposed in this paper is used to realize the fault diagnosis ，in the process of analyzing the simulation signal and experimental signal of the bearing.