Permanent magnet synchronous motors (PMSM) has the advantages of simple structure, small size, high efficiency, and high power factor, and a key dynamic source and is widely used in industry, equipment and electric vehicle. Aiming at its inter-turn short-circuit fault, this paper proposes a fault diagnosis method based on sparse representation and support vector machine (SVM). Firstly, the sparse representation is used to extract the first and second largest sparse coefficients of both current signal and vibration signals, and then they are composed into four-dimensional feature vectors. Secondly, the feature vectors are input into the support vector machine for fault diagnosis, which is suitable for small sample. Experiments on a permanent magnet synchronous motor with artificially set inter-turn short-circuit fault and a normal one showed that the method is feasible and accurate.