Background With the wide application of CT scanning, the separation of pulmonary arteries and veins (A/V) based on CT images plays an important role for assisting surgeons in preoperative planning of lung cancer surgery. However, distinguishing between arteries and veins in chest CT images remains challenging due to the complex structure and the presence of their similarities. Methods We proposed a novel method for automatically separating pulmonary arteries and veins based on vessel topology information and a twin-pipe deep learning network. First, vessel tree topology is constructed by combining scale-space particles and multi-stencils fast marching (MSFM) methods to ensure the continuity and authenticity of the topology. Second, a twin-pipe network is designed to learn the multiscale differences between arteries and veins and the characteristics of the small arteries that closely accompany bronchi. Finally, we designed a topology optimizer that considers interbranch and intrabranch topological relationships to optimize the results of arteries and veins classification. Results The proposed approach is validated on the public dataset CARVE14 and our private dataset. Compared with ground truth, the proposed method achieves an average accuracy of 90.1% on the CARVE14 dataset, and 96.2% on our local dataset. Conclusions The method can effectively separate pulmonary arteries and veins and has good generalization for chest CT images from different devices, as well as enhanced and noncontrast CT image sequences from the same device.