Effective multi-object tracking is still challenging due to the trade-off between tracking accuracy and speed. Because the recent multi-object tracking (MOT) methods leverage object appearance and motion models so as to associate detections between consecutive frames, the key for effective multi-object tracking is to reduce the computational complexity of learning both models. To this end, this work proposes global appearance and motion models to discriminate multiple objects instead of learning local object-specific models. In concrete detail, it learns a global appearance model using contrastive learning between object appearances. In addition, we learn a global relation motion model using relative motion learning between objects. Moreover, this paper proposes object constraint learning for improving tracking efficiency. This study considers the discriminability of the models as a constraint, and learns both models when inconsistency with the constraint occurs. Therefore, object constraint learning differs from the conventional online learning for multi-object tracking which updates learnable parameters per frame. This work incorporates global models and object constraint learning into the confidence-based association method, and compare our tracker with the state-of-the-art methods on public available MOT Challenge datasets. As a result, we achieve 64.5% MOTA (multi-object tracking accuracy) and 6.54 Hz tracking speed on the MOT16 test dataset. The comparison results show that our methods can contribute to improve tracking accuracy and tracking speed together.