Liver cancer remains the main cause of cancer-induced death in the world. Nowadays, vascular interventional therapy is the main treatment method for liver cancer, and vascular imaging plays a key role in this process, providing important reference for professional doctors. However, manual labeling of blood vessels is a complex and time-consuming task, so the automatic segmentation of liver blood vessels is of great significance for related work. In this study, an attention gating unit is introduced to improve the extraction of network information, and a new network structure, UNetR-AGM, is proposed by combining this unit with the UNetR network. The balanced filtering strategy is used for pre-processing abdominal computed tomography (CT), which not only improves the contrast between blood vessels and surrounding tissues but also completes the rough segmentation of blood vessels. To verify the effectiveness of the proposed method, this study compares UNetR-AGM with other research methods on the medical segmentation decathlon (MSD) dataset and analyzes the accuracy of the algorithm. The experimental results show that the method developed in this study is more effective than other models.