Video semantic segmentation is an essential task for the analysis and understanding of videos. Recent efforts largely focus on supervised video segmentation by learning from fully annotated data, but the learnt models often experience clear performance drop while applied to videos of a different domain. This paper presents DA-VSN, a domain adaptive video segmentation network that addresses domain gaps in videos by temporal consistency regularization (TCR) for consecutive frames of target-domain videos. DA-VSN consists of two novel and complementary designs. The first is cross-domain TCR that guides the prediction of target frames to have similar temporal consistency as that of source frames (learnt from annotated source data) via adversarial learning. The second is intra-domain TCR that guides unconfident predictions of target frames to have similar temporal consistency as confident predictions of target frames. Extensive experiments demonstrate the superiority of our proposed domain adaptive video segmentation network which outperforms multiple baselines consistently by large margins.