Person re-identification across cameras remains a very challenging problem, especially when there are no overlapping fields of view between cameras. In this paper, we present a novel multi-channel parts-based convolutional neural network (CNN) model under the triplet framework for person re-identification. Specifically, the proposed CNN model consists of multiple channels to jointly learn both the global full body and local body-parts features of the input persons. The CNN model is trained by an improved triplet loss function that serves to pull the instances of the same person closer, and at the same time push the instances belonging to different persons farther from each other in the learned feature space. Extensive comparative evaluations demonstrate that our proposed method significantly outperforms many state-of-the-art approaches, including both traditional and deep network-based ones, on the challenging i-LIDS, VIPeR, PRID2011 and CUHK01 datasets.