In this paper, a new deep learning network named as graph-based point tracker (GPT) is proposed for 3D object tracking in point clouds. GPT is not based on Siamese network applied to template and search area, but it is based on the transfer of target clue from the template to the search area. GPT is end-to-end trainable. GPT has two new modules: graph feature augmentation (GFA) and improved target clue (ITC) module. The key idea of GFA is to exploit one-to-many relationship between template and search area points using a bipartite graph. In GFA, edge features of the bipartite graph are generated by transferring the target clues of template points to search area points through edge convolution. It captures the relationship between template and search area points effectively from the perspective of geometry and shape of two point clouds. The second module is ITC. The key idea of ITC is to embed the information of the center of the target into the edges of the bipartite graph via Hough voting, strengthening the discriminative power of GFA. Both modules significantly contribute to the improvement of GPT by transferring geometric and shape information including target center from target template to search area effectively. Experiments on the KITTI tracking dataset show that GPT achieves state-of-the-art performance and can run in real-time.