Multi-object tracking (MOT) is a critical task in computer vision, requiring the accurate identification and continuous tracking of multiple objects across video frames. However, current state-of-the-art methods mainly rely on a global optimization technique and multi-stage cascade association strategy, and those approaches often overlook the specific characteristics of assignment task in MOT and useful detection results that may represent occluded objects. To address these challenges, we propose a novel Track-Focused Online Multi-Object Tracker (TrackTrack) with two key strategies: Track-Perspective-Based Association (TPA) and Track-Aware Initialization (TAI). The TPA strategy associates each track with the most suitable detection result by choosing the one with the minimum distance from all available detection results in a track-perspective manner. On the other hand, the TAI method precludes the generation of spurious tracks in the track-aware aspect by suppressing track initialization of detection results that heavily overlap with current active tracks and more confident detection results. Extensive experiments on MOT17, MOT20, and DanceTrack demonstrate that our TrackTrack outperforms current state-of-the-art trackers, offering improved robustness and accuracy across diverse and challenging tracking scenarios.