An adaptive convolutional graph neural network fault diagnosis method is proposed to diagnose aero-engine accessory gearbox faults under intense background noise conditions. Wavelet packet coefficient matrixes, which decompose from the gearbox′s vibration signals by wavelet packets, are defined as graphs containing nodes and edges. An adaptive graph convolution operation is designed based on Chebyshev polynomials, the adaptive graph convolutional kernel is constructed in the graph convolutional networks to improve the fault feature extraction ability of nodes and edges,and enhance the generalization of the model under strong noise conditions. Finally, the fully connected layer is used for feature extraction to achieve fault diagnosis of aero-engine accessory gearbox. The application case shows that the proposed the adaptive graph convolutional networks has an average diagnostic accuracy of 86. 42% for aero-engine accessory magazine fault diagnosis under strong background noise, which is higher than LeNet, ResNet and GCNet models, and can effectively identify faults and be applied to aero-engine accessory magazine fault diagnosis.