Person re-identification is a popular research topic which aims at matching the specific person in a multi-camera network automatically. Feature representation and metric learning are two important issues for person re-identification. In this paper, we propose a novel person re-identification method, which consists of a reliable representation called Semantic Region Representation (SRR), and an effective metric learning with Mapping Space Topology Constraint (MSTC). The SRR integrates semantic representations to achieve effective similarity comparison between the corresponding regions via parsing the body into multiple parts, which focuses on the foreground context against the background interference. To learn a discriminant metric, the MSTC is proposed to take into account the topological relationship among all samples in the feature space. It considers two-fold constraints: the distribution of positive pairs should be more compact than the average distribution of negative pairs with regard to the same probe, while the average distance between different classes should be larger than that between same classes. These two aspects cooperate to maintain the compactness of the intra-class as well as the sparsity of the inter-class. Extensive experiments conducted on five challenging person re-identification datasets, VIPeR, SYSU-sReID, QUML GRID, CUHK03, and Market-1501, show that the proposed method achieves competitive performance with the state-of-the-art approaches.