With the wide applications of the asynchronous induction motor (IM), various kinds of the electrical and the mechanical faults have been appearing, the main ones of which are the inter-turn short circuit of the stator, the broken-bar of the rotor and the air-gap eccentricity. This paper analyzes the current and the torque of the IM under fault conditions as well as providing fault components. Hilbert transform and the support vector machine (SVM) multi-classification method are applied to improve the sensitivity of fault identification and eliminate the interference of the environmental electromagnetic noise. In order to increase the diagnosis accuracy in different applications, the grid search (GS), the genetic algorithm (GA) and the particle swarm algorithm (PSA) are employed for the parameter optimization of the SVM classification prediction model. The simulation and the experimental results verify the proposed analysis and diagnosis method.