For the problem that doctors manually segment the liver tumor from CT image is time-consuming, labor-intensive, and susceptible to subjective judgment, we propose a deeply supervised residual Unet (DSResUnet) that incorporates residual link and deep supervision into Unet for more precise segmentation. The proposed method was evaluated on the public MICCAI 2017 liver segmentation (LiTS) challenge dataset with Dice coefficient, Jaccard coefficient, average symmetrical surface distance (ASSD), 95% Hausdorff distance (HD95), precision and recall. The experimental results show that the results on the above 7 evaluation indicators of liver segmentation with the proposed DS-ResUnet are 96.06%, 95.08%, 92.54%, 1.98 mm, 12.87 mm, 96.11%, and 96.06%, respectively, achieve superior results on almost all metrics to the widely-used Unet (95.71%, 94.52%, 91.91%, 2.41 mm, 14.21 mm, 95.48%, 96.01%). The results on the above 7 evaluation indicators of liver tumor segmentation with the proposed DS-ResUnet are 67.51%, 76.65%, 54.21%, 6.65 mm, 25.34 mm, 80.39%, and 64.27%, respectively, also better than that of the Unet (60.67%, 73.47%, 47.39%, 9.43 mm, 39.38 mm, 79.61%, 58.01%). Therefore, the proposed DS-ResUnet improves the segmentation results and achieves automatic segmentation of liver and liver tumor regions from the 3D abdominal enhanced CT image.