This article presents a tensor multi-task model for person re-identification (Re-ID). Due to discrepancy among cameras, our approach regards Re-ID from multiple cameras as different but related classification tasks, each task corresponding to a specific camera. In each task, we distinguish the person identity as a one-vs-all linear classification problem, where one classifier is associated with a specific person. By constructing all classifiers into a task-specific projection matrix, the proposed method could utilize all the matrices to form a tensor structure, and jointly train all the tasks in a uniform tensor space. In this space, by assuming the features of the same person under different cameras are generated from a latent subspace, and different identities under the same perspective share similar patterns, the high-order correlations, not only across different tasks but also within a certain task, can be captured by utilizing a new type of low-rank tensor constraint. Therefore, the learned classifiers transform the original feature vector into the latent space, where feature distributions across cameras can be well-aligned. Moreover, this model can be incorporated into multiple visual features to boost the performance, and easily extended to the unsupervised setting. Extensive experiments and comparisons with recent Re-ID methods manifest the competitive performance of our method.