Three-dimensional single object tracking (SOT) in dynamic point cloud sequences is a fundamental problem for numerous intelligent systems. In this article, we propose a deep neural architecture named DeepPCT to achieve accurate and robust tracking in sequential point clouds. Instead of relying on the bounding box classification and regression to localize the object, the proposed framework directly formulates the intersection-over-union (IoU) prediction as its objectives for accurate 3-D localization. A Center IoU (CIoU) is further proposed to mitigate the ambiguity of standard IoU. In addition, we also investigate the impact of an additional re-detection module to the overall tracking performance, since tracking failures frequently occur due to the large variations and error accumulation. Experimental results on the KITTI benchmark demonstrate that the proposed tracker achieves competitive performance, with a 3-D precision rate of 63.7% and a 3-D success rate of 45.0%. Moreover, our tracker achieves compelling performance in the wild with severe illumination variations and occlusions, and even outperforms several 2-D counterpart trackers.