Trajectory prediction is critical for applications of planning safe future movements and remains challenging even for the next few seconds in urban mixed traffic. How an agent moves is affected by the various behaviors of its neighboring agents in different environments. To predict movements, we propose an end-to-end generative model named Attentive Maps Encoder Network (AMENet) that encodes the agents motion and interaction information for accurate and realistic multi-path trajectory prediction. A conditional variational auto-encoder module is trained to learn the latent space of possible future paths based on attentive dynamic maps for interaction modeling and then is used to predict multiple plausible future trajectories conditioned on the observed past trajectories. The efficacy of AMENet is validated using two public trajectory prediction benchmarks Trajnet and InD.