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Modern multi-object tracking (MOT) systems usually model the trajectories by associating per-frame detections. However, when camera motion, fast motion, and occlusion challenges occur, it is difficult to ensure long-range tracking or even the tracklet purity, especially for small objects. Although re-identification is often employed, due to noisy partial-detections, similar appearance, and lack of temporal-spatial constraints, it is not only unreliable and time-consuming, but still cannot address the false negatives for occluded and blurred objects. In this paper, we propose an enhanced MOT paradigm, namely Motion-Aware Tracker (MAT), focusing more on various motion patterns of different objects. The rigid camera motion and nonrigid pedestrian motion are blended compatibly to form the integrated motion localization module. Meanwhile, we introduce the dynamic reconnection context module, which aims to balance the robustness of long-range motion-based reconnection, and includes the cyclic pseudo-observation updating strategy to smoothly fill in the tracking fragments caused by occlusion or blur. Additionally, the 3D integral image module is presented to efficiently cut useless track-detection association connections with temporal-spatial constraints. Extensive experiments on MOT16 and MOT17 challenging benchmarks demonstrate that our MAT approach can achieve the superior performance by a large margin with high efficiency, in contrast to other state-of-the-art trackers.