The accurate modeling of the liver vessel network structure is an important prerequisite for developing a preoperative plan for the liver. Considering that extracting liver blood vessels from patient's abdominal computed tomography(CT) images requires several manual operations, this study proposed an automatic segmentation method of liver vessels based on graph cut, thinning, and vascular combination, which can obtain a complete liver vascular network. First, the CT image was preprocessed by grayscale mapping based on sigmoid function, vessel enhancement based on Hessian filter, and denoising based on anisotropic filter to enhance the grayscale contrast between the vascular and non-vascular parts of the liver. Then, the liver vessels were initially segmented based on the improved three-dimensional graph cut algorithm. Based on the obtained liver vascular structure, the vessel centerline of the liver was then extracted by the proposed thinning algorithm that continuously traversed the foreground voxel points and iteratively deleted the simple points. Finally, the combination of vascular centerline optimization was used to predict and link the vascular centerline fractured portion. The under-segmented liver vessels were complemented based on the complete vascular centerline tree. To verify the proposed hepatic vascular segmentation and complementation algorithm, the open 3D Image Reconstruction for Comparison of Algorithm Database (3Dircadb) was applied to test and quantify the results. The results showed that the proposed algorithm can accurately and effectively segment the vascular network structure from abdominal CT images, and the proposed vascular complementation method can restore the true information of under-segmented liver vessels. Graphical abstract A novel hepatic vessel segmentation method from abdominal CT images was proposed, including graph cut algorithm, centerline extraction, and broken vessel completion. First, the graph cut algorithm was used to obtain the initial segmentation result. Then, the centerline of the initial segmentation result was extracted. Finally, the initial segmentation result was optimized through centerline analysis.