A gearbox is a kind of mechanical transmission device. Aiming at the problem of poor state recognition effect caused by the nonlinearity and instability of the complex fault signal of the gearbox, a gearbox complex fault diagnosis method based on multi-scale Weibull dispersion entropy graph neural network (WB-MDEGNN) is proposed. Firstly, the Weibull distribution (WB) is used to linearize and stabilize the vibration signal to obtain more acute gearbox state information. Then, the Multi-scale dispersion entropy (MDE) is used to extract the quantization features of the given sequence. And construct the node feature matrix. Secondly, use the k-nearest neighbor (KNN) algorithm to extract the correlation of node features and construct the edge index matrix. Combine the node feature matrix with the edge index matrix to construct the feature map. Finally, the feature maps are input into the graph neural networks (GNN) model for classification and recognition. The results show that by collecting gearbox data in five states through piezoelectric acceleration sensors and using the WB-MDEGNN model proposed in this paper for complex fault classification and identification of the collected data, the accuracy rate can be increased by 6.07%~11.69% compared with other existing gearbox fault diagnosis methods. Meanwhile, the accuracy and generalization of the model proposed in this paper are tested by adding Gaussian white noise with different signal-to-noise ratios to the original data and public datasets. The complex fault diagnosis performance of the proposed method, the accuracy difference fluctuation range is between 0.97% and 3.38%, and the generalization test can reach 95%. Therefore, this method has better superiority in dealing with the problem of poor state recognition effect caused by signal nonlinearity and instability, providing a new method for the complex fault diagnosis of gearboxes.