Vessel segmentation is widely used to help with vascular disease diagnosis. Vessels reconstructed using existing methods are often not sufficiently accurate to meet clinical use standards. This is because 3D vessel structures are highly complicated and exhibit unique characteristics, including sparsity and anisotropy. In this paper, we propose a novel hybrid deep neural network for vessel segmentation. Our network consists of two cascaded subnetworks performing initial and refined segmentation respectively. The second subnetwork further has two tightly coupled components, a traditional CNN-based U-Net and a graph U-Net. Cross-network multi-scale feature fusion is performed between these two U-shaped networks to effectively support high-quality vessel segmentation. The entire cascaded network can be trained from end to end. The graph in the second subnetwork is constructed according to a vessel probability map as well as appearance and semantic similarities in the original CT volume. To tackle the challenges caused by the sparsity and anisotropy of vessels, a higher percentage of graph nodes are distributed in areas that potentially contain vessels while a higher percentage of edges follow the orientation of potential nearbyvessels. Extensive experiments demonstrate our deep network achieves state-of-the-art 3D vessel segmentation performance on multiple public and in-house datasets.