The fault diagnosis of the gearbox of wind turbines is a crucial task for wind turbine operation and maintenance. Although a convolutional neural network can extract the related information of adjacent sampling points using kernels, traditional deep learning methods have not leveraged related information from points with a large span of vibration signal data. In this article, a novel fast deep graph convolutional network is proposed to diagnose faults in the gearbox of wind turbines. First, the original vibration signals of the wind turbine gearbox are decomposed by wavelet packet, which presents time–frequency features as graphs. Then, graph convolutional networks are introduced to extract the features of points with a large span of the defined graph samples. Finally, the fast graph convolutional kernel and the particular pooling improvement are used to reduce the number of nodes and achieve fast classification. Experiments on two data sets are performed to verify the efficacy of the proposed method.