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In order to extraction of stabilize the characteristics of partial discharge signal of transformer, a method of partial discharge feature extraction based on synchrosqueezing wavelet transform(SWT) and Multi-scale permutation entropy is proposed, and then the characteristics of partial discharge signal are identified and classified by GK fuzzy clustering method. Firstly, the partial discharge signals generated by four typical Transformer faults are decomposed into a set of modal components containing the characteristic information of local discharge. Then, the partial discharge characteristic information of each modal component is quantified by multi-scale permutation entropy, and the average of the multi-scale permutation entropy of each modal component is used as the identification feature vector. Finally, using the standard cluster center of partial discharge samples obtained by GK fuzzy clustering, European proximity was used to classify partial discharge. The proposed method is applied to the experimental data of transformer partial discharge and compared with the recognition method based on wavelet decomposition and empirical modal decomposition. The experimental results show that the proposed method has better classification, and the classification of transformer partial discharge has higher recognition accuracy, the average recognition accuracy is 93.60%.