Prognostics and health management applications rely heavily on predicting industrial equipment’s remaining useful life (RUL). The traditional RUL prediction approaches mainly consider the nonlinear mapping relationship of time series data but rarely consider the structural information of the equipment, resulting in low prediction accuracy. In order to improve the effectiveness of RUL prediction, this paper develops a graph neural network (GNN)-based spatio-temporal fusion attention (STFA) approach. In the proposed approach, a spatial GNN is adopted to fuse spatial features and structural information of the equipment, and a modified attention mechanism is proposed to fuse temporal features. The fused features are then input to a fully connected layer for RUL prediction. Different from existing works, the proposed STFA can combine the information in time and space at the same time and utilize apriori knowledge about the equipment’s structure. Case studies on RUL prediction problems of a turbofan engine and a steam turbine are conducted. The results and comparison demonstrate the superiority of the proposed approach.