In this paper, we propose an original and efficient tree matching algorithm for intra-patient hepatic vascular system registration. Vascular systems are segmented from CT-scan images acquired at different times, and then modeled as trees. The goal of this algorithm is to find common bifurcations (nodes) and vessels (edges) in both trees. Starting from the tree root, edges and nodes are iteratively matched. The algorithm works on a set of match solutions that are updated to keep the best matches thanks to a quality criterion. It is robust against topological modifications due to segmentation failures and against strong deformations. Finally, this algorithm is validated on a large synthetic database containing cases with various deformation and segmentation problems.