In the field of hyperspectral target tracking, the continuous variation in target scale leads to diverse appearances of tracked objects between consecutive frames, resulting in a decline in tracking accuracy. To address the challenge of target scale variations, a Transfomer-based Scale-adaptive Hyperspectral target Tracker (TSHT) is proposed. The method aims to significantly improve the accuracy of hyperspectral target tracking. Firstly, principal component analysis is applied to hyperspectral images to obtain three-band images. Subsequently, the search images is preprocessed by SwinBlock-Crop25, and then the template image and the preprocessed search image are input into the D-swin feature extraction module for the extraction of multi-block and multi-layer deep features. Following that, the obtained features are concatenated and subjected to a self-attention mechanism to better capture critical information about the target at different scales. Finally, through a multi-layer perceptron, the search image features processed by self-attention are mapped to the final target bounding box, completing the target tracking process. Experimental results demonstrate that TSHT exhibits high success rates and accuracy. In comparison with several state-of-the-art trackers, it outperforms the advanced target tracking algorithm MixFormer by 0.9 percentage points in handling challenges related to target scale variations, while maintaining real-time performance.