In recent years, deep learning-based person re-identification (Re-ID) methods have made significant progress. However, the performance of these methods substantially decreases when dealing with occlusion, which is ubiquitous in realistic scenarios. In this article, we propose a novel semantic-aware occlusion-robust network (SORN) that effectively exploits the intrinsic relationship between the tasks of person Re-ID and semantic segmentation for occluded person Re-ID. Specifically, the SORN is composed of three branches, including a local branch, a global branch, and a semantic branch. In particular, the local branch extracts part-based local features, and the global branch leverages a novel spatial-patch contrastive loss (SPC) to extract occlusion-robust global features. Meanwhile, the semantic branch generates a foreground-background mask for a pedestrian image, which indicates the non-occluded areas of the human body. The three branches are jointly trained in a unified multi-task learning network. Finally, pedestrian matching is performed based on the local features extracted from the non-occluded areas and the global features extracted from the whole pedestrian image. Extensive experimental results on a large-scale occluded person Re-ID dataset (i.e., Occluded-DukeMTMC) and two partial person Re-ID datasets (i.e., Partial-REID and Partial-iLIDS) show the superiority of the proposed method compared with several state-of-the-art methods for occluded and partial person Re-ID. We also demonstrate the effectiveness of the proposed method on two general person Re-ID datasets (i.e., Market-1501 and DukeMTMC-reID).