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In addition to considering the recognition difficulty caused by human posture and occlusion, it is also necessary to solve the modal differences caused by different imaging systems in the Visible-Thermal cross-modal person re-identification (VT-ReID) task. In this paper,we propose the Cross-modal Local Shortest Path and Global Enhancement (CM-LSP-GE) modules,a two-stream network based on joint learning of local and global features. The core idea of our paper is to use local feature alignment to solve occlusion problem, and to solve modal difference by strengthening global feature. Firstly, Attention-based two-stream ResNet network is designed to extract dual-modality features and map to a unified feature space. Then, to solve the cross-modal person pose and occlusion problems, the image are cut horizontally into several equal parts to obtain local features and the shortest path in local features between two graphs is used to achieve the fine-grained local feature alignment. Thirdly, a batch normalization enhancement module applies global features to enhance strategy, resulting in difference enhancement between different classes. The multi granularity loss fusion strategy further improves the performance of the algorithm. Finally, joint learning mechanism of local and global features is used to improve cross-modal person re-identification accuracy. The experimental results on two typical datasets show that our model is obviously superior to the most state-of-the-art methods. Especially, on SYSU-MM01 datasets, our model can achieve a gain of 2.89%and 7.96% in all search term of Rank-1 and mAP. The source code will be released soon.