Multiple object tracking (MOT) plays an important role in intelligent video-processing tasks, which aims to detect and track all moving objects in a scene. Joint-detection-and-tracking (JDT) methods are thriving in MOT tasks, because they accomplish the detection and data association in a single stage. However, the slow training convergence and insufficient data association limit the performance of JDT methods. In this paper, the anchor-based query (ABQ) is proposed to improve the design of the JDT methods for faster training convergence. By augmenting the coordinates of the anchor boxes into the learnable queries of the decoder, the ABQ introduces explicit prior spatial knowledge into the queries to focus the query-to-feature learning of the JDT methods on the local region, which leads to faster training speed and better performance. Moreover, a new template matching (TM) module is designed for the JDT methods, which enables the JDT methods to associate the detection results and trajectories with historical features. Finally, a new transformer-based MOT method, ABQ-Track, is proposed. Extensive experiments verify the effectiveness of the two modules, and the ABQ-Track surpasses the performance of the baseline JDT methods, TransTrack. Specifically, the ABQ-Track only needs to train for 50 epochs to achieve convergence, while that for TransTrack is 150 epochs.