Aiming at the difficulty of fault feature extraction and fault identification of distribution transformers, a fault diagnosis method combining vibration signals, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and graph convolution neural networks (GCN) was proposed. Firstly, the vibration signal from the acceleration sensor is processed by CEEMDAN to obtain a set of intrinsic modal functions. Secondly, its marginal spectrum information is taken as the feature vector. Then, an undirected weighted complete graph is constructed for the eigenvector matrix, and an improved gray wolf optimization algorithm is used to optimize the Gaussian kernel bandwidth. Finally, an improved GCN model with multi-channel and multi-connectivity is built for feature secondary mining and fault classification. At the same time, an index called peak factor is added to the model to realize the identification of unknown faults. In the case analysis, the fault simulation of oil-immersed transformer and dry transformer is carried out respectively, and samples of different states are extracted for testing. The experimental results show that the accuracy of the proposed method for oilimmersed transformer and dry transformer fault identification is 97. 73% and 95. 6%, respectively, which is better than the other two comparison methods. In the face of unknown types of faults and operating conditions change, it also has a high ability to identify.