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Despite the remarkable progress in person re-identification (Re-ID), such approaches still suffer from the failure cases where the discriminative body parts are missing. To mitigate this type of failure, we propose a simple yet effective Horizontal Pyramid Matching (HPM) approach to fully exploit various partial information of a given person, so that correct person candidates can be identified even if some key parts are missing. With HPM, we make the following contributions to produce more robust feature representations for the Re-ID task: 1) we learn to classify using partial feature representations at different horizontal pyramid scales, which successfully enhance the discriminative capabilities of various person parts; 2) we exploit average and max pooling strategies to account for person-specific discriminative information in a global-local manner. To validate the effectiveness of our proposed HPM method, extensive experiments are conducted on three popular datasets including Market-1501, DukeMTMCReID and CUHK03. Respectively, we achieve mAP scores of 83.1%, 74.5% and 59.7% on these challenging benchmarks, which are the new state-of-the-arts.