Person re-identification (re-id) suffers from a serious occlusion problem when applied to crowded public places. In this paper, we propose to retrieve a full-body person image by using a person image with occlusions. This differs significantly from the conventional person re-id problem where it is assumed that person images are detected without any occlusion. We thus call this new problem the occluded person re-identitification. To address this new problem, we propose a novel Attention Framework of Person Body (AFPB) based on deep learning, consisting of 1) an Occlusion Simulator (OS) which automatically generates artificial occlusions for full-body person images, and 2) multi-task losses that force the neural network not only to discriminate a person's identity but also to determine whether a sample is from the occluded data distribution or the full-body data distribution. Experiments on a new occluded person re-id dataset and three existing benchmarks modified to include full-body person images and occluded person images show the superiority of the proposed method.