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Making accurate motion prediction of the surrounding traffic agents such as pedestrians, vehicles, and cyclists is crucial for autonomous driving. Recent data-driven motion prediction methods have attempted to learn to directly regress the exact future position or its distribution from massive amount of trajectory data. However, it remains difficult for these methods to provide multimodal predictions as well as integrate physical constraints such as traffic rules and movable areas. In this work we propose a novel two-stage motion prediction framework, Trajectory Proposal Network (TPNet). TPNet first generates a candidate set of future trajectories as hypothesis proposals, then makes the final predictions by classifying and refining the proposals which meets the physical constraints. By steering the proposal generation process, safe and multimodal predictions are realized. Thus this framework effectively mitigates the complexity of motion prediction problem while ensuring the multimodal output. Experiments on four large-scale trajectory prediction datasets, i.e. the ETH, UCY, Apollo and Argoverse datasets, show that TPNet achieves the state-of-the-art results both quantitatively and qualitatively.