With the acceleration of urbanization and the increasing demand for travel, current road traffic is experiencing rapid growth and more complex spatio-temporal logic. Vehicle tracking on roads presents several challenges, including complex scenes with frequent foreground–background transitions, fast and nonlinear vehicle movements, and the presence of numerous unavoidable low-score detection boxes. In this paper, we propose AM-Vehicle-Track, following the proven-effective paradigm of tracking by detection (TBD). At the detection stage, we introduce the lightweight channel block attention mechanism (LCBAM), facilitating the detector to concentrate more on foreground features with limited computational resources. At the tracking stage, we innovatively propose the noise-adaptive extended Kalman filter (NSA-EKF) module to extract vehicles’ motion information while considering the impact of detection confidence on observation noise when dealing with nonlinear motion. Additionally, we borrow the Byte data association method to address unavoidable low-score detection boxes, enabling secondary association to reduce ID switches. We achieve 42.2 MOTA, 51.2 IDF1, and 364 IDs on the test set of VisDrone-MOT with 72 FPS. The experimental results showcase our approach’s highly competitive performance, attaining SOTA tracking performance with a fast speed.