To overcome the shortcomings of the existing methods in the segmentation of liver medical images, an improved U-Net structure for liver medical image segmentation is proposed in this paper. To reduce information loss, the pooling layer features are copied during upsampling. Moreover, a residual network is introduced to refine the initial segmented image circularly to combine high-level features with low-level features. Using a new boundary-sensitive mixed loss function to refine the image, the network can obtain more accurate segmentation results. The experimental results show that the Dice coefficients of the liver images and liver tumor images are 96.26% and 83.32%, respectively. Compared with the traditional U-Net, the proposed network can obtain more advanced semantic information and improve the segmentation accuracy of liver and liver tumor images.