Transmission systems are widely applied in rotating machinery, and the diagnosis of their composite faults is crucial for ensuring the healthy operation of mechanical equipment. In order to improve the accuracy and generalization of transmission compound fault diagnosis, a method of transmission compound fault diagnosis based on multi-domain feature map neural network (MDFGNN) is proposed. Firstly, multiple features of vibration signals are extracted from time domain, frequency domain and entropy to obtain rich multi-feature status information of the transmission, and a node feature matrix is constructed. Then k-nearest neighbor (KNN) algorithm is used to extract the sequence regularity and order of node features, and an edge index matrix is constructed. Secondly, the node feature matrix and the edge index matrix are combined to build the feature map, and the feature map is input into the Graph Neural Networks (GNN) model for classification and recognition. Finally, the accuracy and generalization of the proposed model were tested by adding Gaussian white noise with different signal-to-noise ratios to the original data and the HUST Bearing dataset. In order to verify the effectiveness of the proposed method, a transmission vibration test platform was built, and transmission data of five states were collected by piezoelectric acceleration sensors. The results show that: The multi-domain feature map can fully and comprehensively mine the fault information of the compound fault state of the transmission, overcome the weak, non-linear and complex problems of the compound fault signal, obtain more sensitive information of the transmission operation state, improve the utilization rate of the original data and the stability of the model. Compared with other existing transmission fault diagnosis methods, the accuracy rate can be increased by 4.75%~12.26%, the accuracy difference fluctuation range is 0.07%~1.28%, and the generalization test can reach 96.25%.