•Tracks and detections are modelled as random vectors in which uncertainties are taken into account.•The similarity between track and detection is evaluated based on a modified Kullback-Leibler divergence.•The level of track uncertainty is incorporated in the proposed cost function to guide the data association process.•Code has been made available at https://github.com/hejiawei2023/UG3DMOT. For the benefit of the community. In the existing literature, most 3D multi-object tracking algorithms based on the tracking-by-detection framework employed deterministic tracks and detections for similarity calculation in the data association stage. Namely, the inherent uncertainties existing in tracks and detections are overlooked. In this work, we discard the commonly used deterministic tracks and deterministic detections for data association, instead, we propose to model tracks and detections as random vectors in which uncertainties are taken into account. Then, based on a modified Kullback-Leibler divergence, the similarity between two multidimensional distributions, i.e. track and detection, is evaluated for data association purposes. Lastly, the level of track uncertainty is incorporated in our cost function design to guide the data association process. Comparative experiments have been conducted on two typical datasets, KITTI and nuScenes, and the results indicated that our proposed method outperformed the compared state-of-the-art 3D tracking algorithms. For the benefit of the community, our code has been made available at https://github.com/hejiawei2023/UG3DMOT.