Liver tumors are one of the most aggressive malignancies in the human body. Computer-aided technology and liver interventional surgery are effective in the prediction, identification and management of liver neoplasms. One of the important processes is to accurately grasp the morphological structure of the liver and liver blood vessels. However, accurate identification and segmentation of hepatic blood vessels in CT images poses a formidable challenge. Manually locating and segmenting liver vessels in CT images is time-consuming and impractical. There is an imperative clinical requirement for a precise and effective algorithm to segment liver vessels. In response to this demand, the current paper advocates a liver vessel segmentation approach that employs an enhanced 3D fully convolutional neural network V-Net. The network model improves the basic network structure according to the characteristics of liver vessels. First, a pyramidal convolution block is introduced between the encoder and decoder of the network to improve the network localization ability. Then, multi-resolution deep supervision is introduced in the network, resulting in more robust segmentation. Finally, by fusing feature maps of different resolutions, the overall segmentation result is predicted. Evaluation experiments on public datasets demonstrate that our improved scheme can increase the segmentation ability of existing network models for liver vessels. Compared with the existing work, the experimental outcomes demonstrate that the technique presented in this manuscript has attained superior performance on the Dice Coefficient index, which can promote the treatment of liver tumors.