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Person re-identification (Re-ID) is a classical computer vision task and has achieved great progress so far. Recently, long-term Re-ID with clothes-changing has attracted increasing attention. However, existing methods mainly focus on image-based setting, where richer temporal information is overlooked. In this paper, we focus on the relatively new yet practical problem of clothes-changing video-based person re-identification (CCVReID), which is less studied. We systematically study this problem by simultaneously considering the challenge of the clothes inconsistency issue and the temporal information contained in the video sequence for the person Re-ID problem. Based on this, we develop a two-branch confidence-aware re-ranking framework for handling the CCVReID problem. The proposed framework integrates two branches that consider both the classical appearance features and cloth-free gait features through a confidence-guided re-ranking strategy. This method provides the baseline method for further studies. Also, we build two new benchmark datasets for CCVReID problem, including a large-scale synthetic video dataset and a real-world one, both containing human sequences with various clothing changes. We will release the benchmark and code in this work to the public.