Coupling fault is a common fault in mechanical equipment pattern. In this paper, a graph neural network method is proposed to study the multi-mode fault coupling. Firstly, the wavelet transform is used to preprocess the time series data, then the coupled fault topology is established according to the fault correlation as the input of the graph neural network. Finally, the graph convolutional neural network is used to diagnose the multi-mode coupling fault. The algorithm is tested on the XJTU Gearbox dataset.