We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, self-occlusion, irregular mesh topologies, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling softwares. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we first introduce a robust data preprocessing pipeline that utilizes visibility check and winding mumber to maximize the use of existing 3D data. Leveraging this data, we employ a 3D-native DiT model that directly models the distribution of 3D data in latent space, generating coarse geometries with regular mesh topology in seconds. Subsequently, a normal-based geometry refiner enhances local surface details, which can be applied automatically or interactively with user input. Extensive experiments demonstrate that our method achieves high efficacy in producing superior quality 3D assets compared to existing methods.