This article proposes an improved fault diagnosis strategy to enhance the diagnosis accuracy for the induction motor under the slight fault situation. The additional even and triple harmonics, caused by the faulty asymmetric structure, are taken into account. As a result, the stator current faulty characteristic frequency components, caused by faults from the stator side, the rotor side and the air-gap side, are enlarged. The Hilbert transform and the support vector machine (SVM) multiclassification method are applied to improve the sensitivity of fault identification. To increase the diagnosis accuracy and speediness in different applications, the grid search method, the genetic algorithm and the particle swarm algorithm are employed for the parameter optimization of the SVM classification prediction model. Finally, compared with the traditional strategy, the diagnosis accuracy can be increased by 6%-10% based on the proposed strategy. Comprehensive simulation and experimental results have fully verified the proposed diagnosis method in this article.