The task of multi-object tracking (MOT) aims to detect and associate objects across video frames to obtain their motion trajectories. Unlike traditional tracking-by-detection algorithms, Transformer-based MOT methods accomplish both detection and tracking tasks through the interaction decoding of detect query and track query, showing stronger adaptability to complex scenarios. Unfortunately, the tracking performance of such kind of method is largely constrained by detection performance. The utilization of extra object detectors does improve tracking performance but incurs additional computational burden. Due to its strong capability of multi-scale feature extraction and high detection accuracy, in this paper, we boost a Transformer-based MOT model by integrating the YOLOX object detector into the backbone network and utilizing the feature pyramid structure of the YOLOX to construct an efficient encoder, which improves detection and tracking performance while reduces computational cost. Furthermore, to alleviate the optimization conflicts between the detector and the tracker, an inter-task query interaction module (IQIM) is introduced, significantly enhancing the model performance. A progressive training strategy is also proposed that first pre-trains the object detector to provide high-quality predictions for detect query, and then trains the decoder to expedite model convergence. Experimental results on DanceTrack dataset show that the proposed MOT method achieves promising tracking performances, reaching the HOTA score of 70.7%, the AssA of 60.7%, and the IDF1 metric of 72.6%, outperforms other Transformer-based methods.