Discriminative feature representation of person image is important for person re-identification (Re-ID) task. Recently, attributes have been demonstrated beneficially in guiding for learning more discriminative feature representations for Re-ID. As attributes normally co-occur in person images, it is desirable to model the attribute dependencies to improve the attribute prediction and thus Re-ID results. In this paper, we propose to model these attribute dependencies via a novel attribute knowledge graph (AttKG), and propose a novel Attribute Knowledge Graph Convolutional Network (AttKGCN) to solve Re-ID problem. AttKGCN integrates both attribute prediction and Re-ID learning together in a unified end-to-end framework which can boost their performances, respectively. AttKGCN first builds a directed attribute KG whose nodes denote attributes and edges encode the co-occurrence relationships of different attributes. Then, AttKGCN learns a set of inter-dependent attribute classifiers which are combined with person visual descriptors for attribute prediction. Finally, AttKGCN integrates attribute description and deeply visual representation together to construct a more discriminative feature representation for Re-ID task. Extensive experiments on several benchmark datasets demonstrate the effectiveness of AttKGCN on attribute prediction and Re-ID tasks.