3D single object tracking remains a challenging problem due to the sparsity and incompleteness of the point clouds. Existing algorithms attempt to address the challenges in two strategies. The first strategy is to learn dense geometric features based on the captured sparse point cloud. Nevertheless, it is quite a formidable task since the learned dense geometric features are with high uncertainty for depicting the shape of the target object. The other strategy is to aggregate the sparse geometric features of multiple templates to enrich the shape information, which is a routine solution in 2D tracking. However, aggregating the coarse shape representations can hardly yield a precise shape representation. Different from 2D pixels, 3D points of different frames can be directly fused by coordinate transform, i.e., shape completion. Considering that, we propose to construct a synthetic target representation composed of dense and complete point clouds depicting the target shape precisely by shape completion for robust 3D tracking. Specifically, we design a voxelized 3D tracking framework with shape completion, in which we propose a quality-aware shape completion mechanism to alleviate the adverse effect of noisy historical predictions. It enables us to effectively construct and leverage the synthetic target representation. Besides, we also develop a voxelized relation modeling module and box refinement module to improve tracking performance. Favorable performance against state-of-the-art algorithms on three benchmarks demonstrates the effectiveness and generalization ability of our method.