For computer-aided diagnosis of cardiovascular diseases, accurately extracted centerlines of coronary arteries are important. However, centerlines extracted from incorrectly segmented vessels are usually unsatisfactory. For this reason, we propose two automatic centerline correction methods in this paper. First, a method based on the local volume comparison and the morphological comparison is presented to remove false centerlines from over-segmented tissues. Second, another method based on the judgment of vessel identity and the gradient-SDF (source distance field) calculation is presented to add missing centerlines of under-segmented vessels. We have validated the proposed centerline correction methods on real CT angiographic datasets of coronary arteries. The quantitative evaluation results show that the proposed methods can effectively correct centerline errors arising from erroneous vessel segmentation in most cases.