Abstract: Remaining useful life (RUL) prediction is an important process of prediction and health management ( PHM ). Traditional CNN, RNN and GNN mainly focus on the time dependence of RUL multivariate time series (MTS), ignoring the spatial dependence, or capturing the spatial dependence and time dependence respectively, and cannot capture the correlation between different sensors at different timestamps ( DEDT ). To address this problem, we propose a fully connected spatio-temporal graph neural network method, which includes two key parts: FC graph construction and FC graph convolution. For the construction of the graph, we design an attenuation graph according to the temporal distance between the sensors to connect the sensors on all timestamps, and model the ST dependency fully modeled by considering the correlation between DEDTs. In addition, we design a FC graph convolution with a mobile pooling GNN layer to effectively capture ST dependencies and learn effective representations, avoiding the high computational complexity of global graph convolution. In addition, temporal pooling is employed to dynamically extract high-level features, thereby improving the generalization ability of the model. A number of experiments such as comparative simulation and ablation simulation are carried out on the NASA C-MAPSS aero-engine MTS benchmark dataset. The results show that the proposed method is superior to the existing advanced methods, offering a new solution for RUL prediction.