Abstract: In order to improve the accuracy of partial discharge (PD) diagnosis by making full use of the local features of PD signal and the correlation between those local features, a novel PD diagnosis method based on graph signal and graph convolutional network (GCN) was proposed in this paper. Firstly, this method selected the time-frequency (T-F) spectrum of PD pulse to construct the graph signal. In detail, it took the sub-matrixes of the T-F spectrum gray matrix as the graph nodes namely local features while the spatial adjacency and the features similarity of nodes were regarded as the principles of matching the neighbors for each node, which formed the topology between different nodes and enriched the data information of T-F spectrum. Then, the GCN, which adopting the nodes' features and graph topology together as inputs, was arranged to learn the PD features and identify the PD types. The experimental results show that the proposed method can effectively diagnose PD types. Compared with the traditional deep learning methods, it has richer information of PD T-F spectrum and higher recognition accuracy. Moreover, with the reduction of sample size, the advantage is more obvious.