By analyzing the shortcomings of the common method for bearing fault diagnosis, a new method 〖HJ*4/9〗based on correlation matching is proposed. With the kinetic model of rolling element bearing with fault, the analytic model for faulty impulse is set and used as the matching atom with parameters optimized by a series of indexes, such as spectrum kurtosis, kurtosis, smoothness index, and correlation coefficient. The optimal periodical impulse model is used to approach the periodic faulty impulse in the vibration signal of the bearing, which is processed in the time domain. In this method, the problem of over- or insufficient decomposition in standard matching pursuit is solved, and the faulty impulse is accurately extracted, which is helpful for the quantitative analysis of the faulty bearing. Both simulations and experiments indicate that the proposed method is effective for bearing fault diagnosis.