Advancements in 3D vision have increased the impact of blood vessel modeling on medical applications. However, accurately representing the complex geometry and topology of blood vessels remains a challenge due to their intricate branching patterns, curvatures, and irregular shapes. In this study, we propose a hierarchical part-based frame work for 3D vessel generation that separates the global binary tree-like topology from local geometric details. Our approach proceeds in three stages: (1) key graph generation to model the overall hierarchical struc ture, (2) vessel segment generation conditioned on geometric properties, and (3) hierarchical vessel assembly by integrating the local segments according to the global key graph. We validate our framework on real world datasets, demonstrating superior performance over existing methods in modeling complex vascular networks. This work marks the first successful application of a part-based generative approach for 3D vessel modeling, setting a new benchmark for vascular data generation. The code is available at: https://github.com/CybercatChen/PartVessel.git.