In the process of person re-identification (ReID), the disparity of various datasets caused by different cameras and viewing distances poses challenges. Additionally, the inherent limitation of convolutional neural networks (CNNs) in capturing long-range dependencies exacerbates these challenges. To address these issues, this paper proposes the Triple Streams with Pos-insertion Transformer ReID (TSPT ReID) based on the Transformer architecture. The key design of TSPT ReID, the Triple Streams Transformer Encoder (TST Encoder), establishes multi-head attention layers on three different scales to enhance the correlation between various scales. To enhance the recognizability and robustness of valid pedestrian edges, the Shift Pos-insertion Module (SPI Module) is introduced by adding shift-based position coding in the attention layers without introducing additional parameters. The experimental results show the effectiveness of the model on multiple datasets, achieving 82.9% mAP and 91.4% Rank-1 accuracy on the DukeMTMC, and 83.5% mAP and 85.9% Rank-1 accuracy on CUKH03.