Compact feature representation of person image is important for person re-identification (Re-ID) task. Recently, part-based representation models have been widely studied for extracting the more compact and robust feature representation for person image to improve person Re-ID results. However, existing part-based representation models mostly extract the features of different parts independently which ignore the spatial relationship information among different parts. To address this issue, 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 spatial relationships among different parts. Then, both local and global feature learning are achieved by the feature information passing in PH-GCN, which takes the information of other parts 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 representation and learning. Extensive experiments on several widely used benchmark datasets demonstrate the effectiveness and benefits of the proposed PH-GCN approach for person Re-ID task.