To safely and rationally participate in dense and heterogeneous traffic, autonomous vehicles require to sufficiently analyze the motion patterns of surrounding traffic-agents and accurately predict their future trajectories. This is challenging because the trajectories of traffic-agents are not only influenced by the traffic-agents themselves but also by spatial interaction with each other. Previous methods usually rely on the sequential step-by-step processing of Long Short-Term Memory networks (LSTMs) and merely extract the interactions between spatial neighbors for single type traffic-agents. We propose the Spatio-Temporal Transformer Networks (S2TNet), which models the spatio-temporal interactions by spatio-temporal Transformer and deals with the temporel sequences by temporal Transformer. We input additional category, shape and heading information into our networks to handle the heterogeneity of traffic-agents. The proposed methods outperforms state-of-the-art methods on ApolloScape Trajectory dataset by more than 7\% on both the weighted sum of Average and Final Displacement Error. Our code is available at https://github.com/chenghuang66/s2tnet.