As an important area in computer vision, object tracking has formed two separate communities that respectively study Single Object Tracking (SOT) and Multiple Object Tracking (MOT). However, current methods in one tracking scenario are inflexible to the other due to the divergence in the training datasets and tracker designs in both tasks. Although UniTrack demonstrates that a shared appearance model with multiple heads can be used to tackle individual tracking tasks, it fails to exploit the large-scale tracking datasets for training and performs poorly on the single object tracking. A track transformer is developed in our UTT to predict the target localization in tracking frames given previous frame features and target localization, which can be either the specified box in SOT or the detected boxes in MOT. Inside the track transformer, the correlation between the target feature and the tracking frame feature is exploited to update target representation for predicting localization. We demonstrate that both SOT and MOT tasks can be solved within this framework, and the model can be simultaneously end-to-end trained by alternatively optimizing the SOT and MOT objectives on the datasets of individual tasks. Extensive experiments are conducted on several benchmarks with a unified model trained on both SOT and MOT datasets.