Predicting the future trajectories of nearby objects plays a pivotal role in Robotics and Automation such as autonomous driving. While learning-based trajectory prediction methods have achieved remarkable performance on public benchmarks, the generalization ability of these approaches remains questionable. The poor generalizability on unseen domains, a well-recognized defect of data-driven approaches, can potentially harm the real-world performance of trajectory prediction models. We are thus motivated to improve generalization ability of models instead of merely pursuing high accuracy on average. Due to the lack of benchmarks for quantifying the generalization ability of trajectory predictors, we first construct a new benchmark called argoverse-shift, where the data distributions of domains are significantly different. Using this benchmark for evaluation, we identify that the domain shift problem seriously hinders the generalization of trajectory predictors since state-of-the-art approaches suffer from severe performance degradation when facing those out-of-distribution scenes. To enhance the robustness of models against domain shift problems, we propose a plug-and-play strategy for domain normalization in trajectory prediction. Our strategy utilizes the Frenet coordinate frame for modeling and can effectively narrow the domain gap of different scenes caused by the variety of road geometry and topology. Experiments show that our strategy noticeably boosts the prediction performance of the state-of-the-art in domains that were previously unseen to the models, thereby improving the generalization ability of data-driven trajectory prediction methods.