Vehicle re-identification (re-ID) is of great significance to urban operation, management, security and has gained more attention in recent years. However, two critical challenges in vehicle re-ID have primarily been underestimated, ie, 1): how to make full use of raw data, and 2): how to learn a robust re-ID model with noisy data. In this paper, we first create a video vehicle re-ID evaluation benchmark called VVeRI-901 and verify the performance of video-based re-ID is far better than static image-based one. Then we propose a new Pompeiu-hausdorff distance (PhD) learning method for video-to-video matching. It can alleviate the data noise problem caused by the occlusion in videos and thus improve re-ID performance significantly. Extensive empirical results on video-based vehicle and person re-ID datasets, ie, VVeRI-901, MARS and PRID2011, demonstrate the superiority of the proposed method. The source code of our proposed method is available at https://github. com/emdata-ailab/PhD-Learning.