In order to solve the problems of high failure rate of asynchronous motor and difficult to identify the fault category effectively, a fault diagnosis method based on the approximate entropy and support vector machine（SVM） was proposed. By constructing the fault simulation and reconstruction test, the multipoint vibration signal samples of four different states were measured. The approximate entropy sample values were calculated by using the approximate entropy algorithm, and the approximate entropy fault feature vectors of the four different states were obtained. Combined with SVM algorithm, the SVM classification model was built. The approximate entropy feature quantity was divided into training samples and test samples, the fault diagnosis accuracy was 97.5%. However, the accuracy of improved BP neural network diagnosis method was 92.5%. The results show that the method of approximate entropy combined with support vector machine has higher diagnostic accuracy.