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In order to solve the problem of accurate segmentation of liver and liver tumor in computed tomography(CT) images, a liver segmentation algorithm based on 3D full convolution network and a liver tumor segmentation algorithm is proposed. Both the liver segmentation algorithm and the liver tumor segmentation algorithm are based on the Vnet network. In the liver segmentation algorithm, the morphological method is used for post-processing, which improves the liver segmentation accuracy. In the liver tumor segmentation algorithm, the combined loss function is used to train the Vnet network, which makes the Vnet network better converge. Post-processing is used to improve the liver tumor segmentation accuracy. In order to verify the performance of the algorithm, a 5-fold cross-validation experiment of liver segmentation and liver tumor segmentation was performed using the MICCAI 2017 Liver Tumor Segmentation Challenge (LiTS) dataset. The average segmentation accuracy of the liver segmentation algorithm in the test set was 0.9510, which was higher than that of the Unet network and the 3D Unet network; the average segmentation accuracy of the liver tumor segmentation algorithm was 0.712. The experimental results show that the liver segmentation algorithm can accurately segment the liver, and the liver tumor segmentation algorithm also achieves a high accuracy.