Preoperative observation of liver status in patients with liver tumors by abdominal Computed Tomography (CT) imaging is one of the essential references for formulating surgical plans. Preoperative vessel segmentation in the patient's liver region has become an increasingly important and challenging problem. Almost all existing methods first segment arterial and venous vessels on CT in the arterial and venous phases, respectively. Then, the two are directly registered to complete the reconstruction of the vascular system, ignoring the displacement and deformation of blood vessels caused by changes in body position and respiration in the two phases. We propose an unsupervised domain-adaptive two-stage vessel segmentation framework for simultaneous fine segmentation of arterial and venous vessels on venous phase CT. Specifically, we first achieve domain adaptation for arterial and venous phase CT using a modified cycle-consistent adversarial network. The newly added discriminator can improve the ability to generate and discriminate tiny blood vessels, making the domain-adaptive network more robust. The second-stage supervised training of arterial vessels was then performed on the translated arterial phase CT. In this process, we propose an orthogonal depth projection loss function to enhance the representation ability of the 3D U-shape segmentation network for the geometric information of the vessel model. The segmented venous vessels were also performed on venous phase CT in the second stage. Finally, we invited professional doctors to annotate arterial and venous vessels on the venous phase CT of the test set. The experimental results show that the segmentation accuracy of arterial and venous vessels on venous phase CT is 0.8454 and 0.8087, respectively. Our proposed framework can simultaneously achieve supervised segmentation of venous vessels and unsupervised segmentation of arterial vessels on venous phase CT. Our approach can be extended to other fields of medical segmentation, such as unsupervised domain adaptive segmentation of liver tumors at different CT phases, to facilitate the development of the community.