Person re-identification (ReID) is a challenging task due to arbitrary human pose variations, background clutters, etc. It has been studied extensively in recent years, but the multifarious local and global features are still not fully exploited by either ignoring the interplay between whole-body images and body-part images or missing in-depth examination of specific body-part images. In this paper, we propose a novel attention-driven multi-branch network that learns robust and discriminative human representation from global whole-body images and local body-part images simultaneously. Within each branch, an intra-attention network is designed to search for informative and discriminative regions within the whole-body or body-part images, where attention is elegantly decomposed into spatial-wise attention and channel-wise attention for effective and efficient learning. In addition, a novel inter-attention module is designed which fuses the output of intra-attention networks adaptively for optimal person ReID. The proposed technique has been evaluated over three widely used datasets CUHK03, Market-1501 and DukeMTMC-ReID, and experiments demonstrate its superior robustness and effectiveness as compared with the state of the arts.