To effectively extract the partial discharge fault feature and diagnose the fault of a power transformer, this paper presents a method based on empirical wavelet transform (EWT) and multiscale quantum entropy (MQE) to diagnose transformer faults. First, EWT is employed for partial discharge signal decomposition to get different IMF components and a residual. Secondly, the MQE sequence of each IMF is generated by signal decomposition. Then the dimension of the MQE sequence is reduced with the local tangent space arrangement algorithm (LTSA). Finally, a hierarchical clustering algorithm (HAC) is used for clustering analysis to get the recognition results of different types of discharge. Compared with different diagnostic methods, the effectiveness and superiority of the proposed method is verified by the simulation result and experimental data. This work is supported by the National Natural Science Foundation of China (No. SGLNDK00KJJS1500008).