Transformers have proven superior performance for a wide variety of tasks since they were introduced. In recent years, they have drawn attention from the vision community in tasks such as image classification and object detection. Despite this wave, an accurate and efficient multiple-object tracking (MOT) method based on transformers is yet to be designed. We argue that the direct application of a transformer architecture with quadratic complexity and insufficient noise-initialized sparse queries - is not optimal for MOT. We propose TransCenter, a transformer-based MOT architecture with dense representations for accurately tracking all the objects while keeping a reasonable runtime. Methodologically, we propose the use of image-related dense detection queries and efficient sparse tracking queries produced by our carefully designed query learning networks (QLN). On one hand, the dense image-related detection queries allow us to infer targets' locations globally and robustly through dense heatmap outputs. On the other hand, the set of sparse tracking queries efficiently interacts with image features in our TransCenter Decoder to associate object positions through time. As a result, TransCenterexhibits remarkable performance improvements and outperforms by a large margin the current state-of-the-art methods in two standard MOT benchmarks with two tracking settings (public/private). TransCenter is also proven efficient and accurate by an extensive ablation study and, comparisons to more naive alternatives and concurrent works. The code is made publicly available at https://github.com/yihongxu/transcenter.