Object detection is widely used in objecttracking; anchor-free object tracking provides an end-to-end single-object-tracking approach. In thisstudy, we propose a new anchor-free network, the Siamese center-prediction network (SiamCPN). Given the presence of referenced object features in the initial frame, we directly predict the center point and size of the object in subsequent frames in a Siamese-structure network without the need for per-frame post-processing operations. Unlike other anchor-free tracking approaches that are based on semantic segmentation and achieve anchor-free tracking by pixel-level prediction, SiamCPN directly obtains all information required for tracking, greatly simplifying the model. A center-prediction sub-network is applied to multiple stages of the backbone to adaptively learn from the experience of different branches of the Siamese net. The model can accurately predict object location, implement appropriate corrections, and regress the size of the target bounding box. Compared to other leading Siamese networks, SiamCPN is simpler, faster, and more efficient as it uses fewer hyperparameters. Experiments demonstrate that our method outperforms other leading Siamese networks on GOT-10K and UAV123 benchmarks, and is comparable to other excellent trackers on LaSOT, VOT2016, and OTB-100 while improving inference speed 1.5 to 2 times.