Person re-identification (re-ID) tackles the problem of matching person images with the same identity from different cameras. In practical applications, due to the differences in camera performance and distance between cameras and persons of interest, captured person images usually have various resolutions. This problem, named Cross-Resolution Person Re-identification, presents a great challenge for the accurate person matching. In this paper, we propose a Deep High-Resolution Pseudo-Siamese Framework (PS-HRNet) to solve the above problem. Specifically, we first improve the VDSR by introducing existing channel attention (CA) mechanism and harvest a new module, i.e., VDSR-CA, to restore the resolution of low-resolution images and make full use of the different channel information of feature maps. Then we reform the HRNet by designing a novel representation head, HRNet-ReID, to extract discriminating features. In addition, a pseudo-siamese framework is developed to reduce the difference of feature distributions between low-resolution images and high-resolution images. The experimental results on five cross-resolution person datasets verify the effectiveness of our proposed approach. Compared with the state-of-the-art methods, the proposed PS-HRNet improves the Rank-1 accuracy by 3.4%, 6.2%, 2.5%,1.1% and 4.2% on MLR-Market-1501, MLR-CUHK03, MLR-VIPeR, MLR-DukeMTMC-reID, and CAVIAR datasets, respectively, which demonstrates the superiority of our method in handling the Cross-Resolution Person Re-ID task. Our code is available at https://github.com/zhguoqing.