Compared with two-dimensional (2D) multi-object tracking (MOT) algorithms, three-dimensional (3D) multi-object tracking algorithms have more research significance and broad application prospects in the unmanned vehicles research field. Aiming at the problem of 3D multi-object detection and tracking, in this paper, the multi-object tracker CenterTrack, which focuses on 2D multi-object tracking task while ignoring object 3D information, is improved mainly from two aspects of detection and tracking, and the improved network is called CenterTrack3D. In terms of detection, CenterTrack3D uses the idea of attention mechanism to optimize the way that the previous-frame image and the heatmap of previous-frame tracklets are added to the current-frame image as input, and second convolutional layer of the hm output head is replaced by dynamic convolution layer, which further improves the ability to detect occluded objects. In terms of tracking, a cascaded data association algorithm based on 3D Kalman filter is proposed to make full use of the 3D information of objects in the image and increase the robustness of the 3D multi-object tracker. The experimental results show that, compared with the original CenterTrack and the existing 3D multi-object tracking methods, CenterTrack3D achieves 88.75% MOTA for cars and 59.40% MOTA for pedestrians and is very competitive on the KITTI tracking benchmark test set.