Video-based person re-identification (re-id) is an important application in practice. Since large variations exist between different pedestrian videos, as well as within each video, it's challenging to conduct re-identification between pedestrian videos. In this paper, we propose a simultaneous intra-video and inter-video distance learning (SI2DL) approach for video-based person re-id. Specifically, SI2DL simultaneously learns an intravideo distance metric and an inter-video distance metric from the training videos. The intra-video distance metric is used to make each video more compact, and the inter-video one is used to ensure that the distance between truly matching videos is smaller than that between wrong matching videos. Considering that the goal of distance learning is to make truly matching video pairs from different persons be well separated with each other, we also propose a pair separation based SI2DL (P-SI2DL). P-SI2DL aims to learn a pair of distance metrics, under which any two truly matching video pairs can be well separated. Experiments on four public pedestrian image sequence datasets show that our approaches achieve the state-of-the-art performance.