Accurate segmentation of three-dimensional (3D) vascular structures from TOF-MRA images is crucial for the diagnosis and interventional treatment of cerebrovascular diseases. However, current 3D segmentation algorithms often result in numerous false positives, where non-vascular or non-target vascular regions are incorrectly segmented. Additionally, the segmented vessels frequently exhibit poor continuity. To address these issues, we propose a simple yet effective two-stage 3D vessel segmentation network. In the first stage, a hybrid CNN-Transformer network is designed to achieve 3D vessel segmentation. In the second stage, another standalone network is employed to refine the segmentation results from the first stage, yielding more accurate outcomes. This second-stage network is trained independently using a corrupt-reconstruct approach, which endows it with the ability to enhance segmentation results. A TOF-MRA dataset has been constructed and extensive experiments have been carried out. The experimental results demonstrate that the proposed method significantly enhances 3D vessel segmentation performance, offering potential benefits for the diagnosis and interventional treatment of intracranial diseases. Moreover, the proposed method is flexible and can be extended to new models by altering or improving specific components within the two-stage framework, providing new insights for future research on 3D vessel segmentation.