Transformer-based trackers have remarkable potential in object tracking and achieve impressive performance. As a crucial element of Transformer, traditional self-attention calculates the similarity between each pixel and all other pixels and obtains powerful representation capability while resulting in excessive computational costs ( \(O(N^2)\) ). In addition, existing tracking frameworks are mainly two-stream and two-stage, which separately extract the features of the target templates and search areas and then perform feature fusion. The obtained features limit the ability to perceive the target effectively. In this paper, we first design a novel attention calculation method and propose a double softmax attention module (DSAM) to achieve an optimal balance between computational efficiency and representational capability. DSAM efficiently reduces the computation complexity from \(O(N^2)\) to O(N). Upon DSAM, we integrate the feature extraction and feature fusion together. Then, we propose a novel one-stream one-stage tracking method (called DSATrack). DSATrack achieves superior performance on six challenging benchmarks. Particularly, it achieves an AUC score of \(65.4\%\) on LaSOT, a normalized precision score of \(85.9\%\) on TrackingNet, and a precision score of \(89.5\%\) on UAV123. The codes are available at https://github.com/WangJun-CV/DSATrack.