Many Multi-Object Tracking (MOT) approaches exploit motion information to associate all the detected objects across frames. However, traditional tracking-by-detection (TBD) methods, relying on the Kalman Filter, often work well in linear motion scenarios but struggle to accurately predict the locations of objects undergoing complex and non-linear movements. To overcome these limitations, we propose ETTrack, a novel motion prediction method with an enhanced temporal motion predictor. Specifically, the motion predictor integrates a transformer model and a Temporal Convolutional Network (TCN) to capture both long-term and short-term motion patterns, and it predicts the future motion of individual objects based on the historical motion information. Additionally, we propose a novel Momentum Correction Loss function that provides additional information regarding the motion direction of objects during training. This allows the motion predictor to rapidly adapt to sudden motion variations and more accurately predict future motion. Our experimental results demonstrate that ETTrack achieves a competitive performance compared with state-of-the-art trackers on DanceTrack and SportsMOT, scoring 56.4$$\%$$
%
and 74.4$$\%$$
%
in HOTA metrics, respectively. Our work provides a robust solution for MOT in complex dynamic environments, which enhances the non-linear motion prediction capabilities of tracking algorithms.