The analysis of Hepatic Portal Vein (HPV) is important in liver surgical planning and diseases diagnosis, such as living-related liver transplant and oncologic resections. Skeletonization is always the necessary way for vasculature quantification analysis. In this paper, we presented an automatic skeletonization algorithm for 3D HPV based on 3D topological thinning. Since the topological thinning method cannot avoid rings, we analyzed the three types of ring and utilized the graph analysis to remove the loop. To effectively prune artificial twigs resulting from the coarse boundary, the developed approach not only takes into account the length of branches but also the radius of the start and the end points. Also this approach adopts the direction change between the branches to distinguish the other vascular systems. This method has been implemented in physical phantoms and human abdominal Multi-slice Spriral CT Angiography (MSCTA). For the variety of image data about HPV, some other vasculare' branches cannot be removed, we will extend our work to add user intervention for easily modification.