In the crowd navigation, reinforcement learning based on graph neural network is a promising method, which effectively solves the poor navigation effect based on social interaction model and the freezing behavior of robot in extreme cases. However, since the information correlation of human trajectory has not been involved in the method, its performance still needs improvement. Therefore, we proposed a deep reinforcement learning model based on Social Spatial–Temporal Graph Convolution Network (SSTGCN) to handle the crowd navigation problem, in which the spatial–temporal information of human trajectory has been taken advantage to predict human behavior intentions and help robot plan path more efficiently. The model consists of graph learning module and robot forward planning module. In the graph learning module, the latent features of agents are taken advantage to reason about the relations among the agents, and SSTGCN is used to update feature matrix. In addition, value estimation module calculates state representation and state prediction module predicts the next state. The robot forward planning module makes use of k-step planning to estimate the quality of state and searches the best k steps planning. We tested our model in the Crowd-Nav platform, and the results show that our model has high navigation success rate and short navigation time. In addition, it has good robustness to crowd changes.