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Object re-identification (re-id) aims to identify a specific object across times or camera views, with the person re-id and vehicle re-id as the most widely studied applications. Re-id is challenging because of the variations in viewpoints, (human) poses, and occlusions. Multi-shots of the same object can cover diverse viewpoints/poses and thus provide more comprehensive information. In this paper, we propose exploiting the multi-shots of the same identity to guide the feature learning of each individual image. Specifically, we design an Uncertainty-aware Multi-shot Teacher-Student (UMTS) Network. It consists of a teacher network (T-net) that learns the comprehensive features from multiple images of the same object, and a student network (S-net) that takes a single image as input. In particular, we take into account the data dependent heteroscedastic uncertainty for effectively transferring the knowledge from the T-net to S-net. To the best of our knowledge, we are the first to make use of multi-shots of an object in a teacher-student learning manner for effectively boosting the single image based re-id. We validate the effectiveness of our approach on the popular vehicle re-id and person re-id datasets. In inference, the S-net alone significantly outperforms the baselines and achieves the state-of-the-art performance.