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Person re-identification (REID) is an important task in video surveillance and forensics applications. Many previous works often build models on the assumption that they have same resolution cross different camera views, while it is divorced from reality. To increase the adaptability of person REID models, this paper focuses on the low-resolution person REID task to relax the impractical assumption when traditional low-resolution person REID models are under pixel-to-pixel supervision in low and high resolution pedestrian image pairs. In addition, they are easily influenced by the global background, illumination or pose variations across camera views. Therefore, we propose a Part-based Enhanced Super Resolution (PESR) network by employing a part division strategy and an enhanced generative adversarial network to boost the unpaired pedestrian image super resolution process. Specifically, the part-based super resolution network transforms low resolution image in probe into high resolution without any pixel-to-pixel supervision and the part-based synthetic feature extractor module can learn discriminative pedestrian feature representation for the generated high resolution images, which employ a part feature connection loss as constraint to conduct matching for person re-identification. Furthermore, evaluations on four public person REID datasets demonstrate the advantages of our method over the state-of-the-art ones.