The person re-identification (Re-ID) task requires to robustly extract feature representations for person images. Recently, part-based representation models have been widely studied for extracting the more compact and robust feature representations for person images to improve person Re-ID results. However, existing part-based representation models mostly extract the features of different parts independently which ignore the relationship information between different parts. To overcome this limitation, in this paper we propose a novel deep learning framework, named Part-based Hierarchical Graph Convolutional Network (PH-GCN) for person Re-ID problem. Given a person image, PH-GCN first constructs a hierarchical graph to represent the pairwise relationships among different parts. Then, both local and global feature learning are performed by the messages passing in PH-GCN, which takes other nodes information into account for part feature representation. Finally, a perceptron layer is adopted for the final person part label prediction and re-identification. The proposed framework provides a general solution that integrates local, global and structural feature learning simultaneously in a unified end-to-end network. Extensive experiments on several benchmark datasets demonstrate the effectiveness of the proposed PH-GCN based Re-ID approach. I. INTRODUCTION Person re-identification (Re-ID) is an active research problem in computer vision [1], [2], [3], [4], [5], [6], [7], [8]. Many of existing Re-ID methods adopt a person classification framework which aims to determine the label of an input person image by using a classifier trained on the training samples [1], [9], [10], [2], [5], [11]. Although recent years have witnessed rapid advancements in person Re-ID, it is still a challenging task partly due to large changes of person appearance caused by variety of factors, such as pose, illumination, deformation and occlusion. One main issue for Re-ID problem is to develop a compact and robust feature representation for person images. Recently, part-based methods have been widely studied and verified beneficially to person Re-ID task [12], [9], [13], [11], [1], [14], [15]. These methods generally conduct feature representation on part-level and thus can extract both local and global discriminative representations for person image. In particular, deeply-learned features have been verified stronger discriminative ability, especially when aggregated from deeply-learned part features [9], [12], [11], [15], [16]. For example, Zhao et al. [12] develop a human part-aligned representation for Re-ID. Sun et al. [11] propose Part-based Convolutional Baseline (PCB) for learning part-level features. Wei et al. [14] propose