As a challenging visual task, visual object tracking has recently been composed of the classification and regression subtasks. The anchor-free regression network gets rid of the dependence on the anchors, but the redundant range makes it usually regress some samples involving non-target information. Evenly dividing a target by the regular receptive field often causes ambiguous target localization. To address these issues, we propose a regression-selective feature-adaptive tracker (RSFA), where the regression-selective subnetwork can not only free the regression task from anchors, but can also select more effective regression samples using the refined criterion. The proposed feature-adaptive strategy concentrates the classification subnetwork on target feature extraction via adaptively modifying the receptive field, and the attached centrality branch offers a correction for target localization by exploiting the spatial information. Additionally, the designed online update mechanism realizes the tracker's online optimization, improving robustness against target deformation. Extensive experiments are conducted on challenging benchmarks, including GOT10 K, OTB2015, UAV123, NFS, VOT2018, VOT2019 and VOT2020-ST. Our tracker achieves satisfactory tracking results, and the evaluations of its tracking performance rank first or second in comparison with the state-of-the-art tracking algorithms.