Liver is the main organ of human metabolic function. At present, the main problems of machine learning in the semantic segmentation of liver images are as follows:1) there are inferior vena cava, soft tissue and blood vessels in the middle of the liver, and even some necrosis or hepatic fissures; 2) the boundary between the liver and some adjacent organs is blurred and difficult to distinguish. In order to solve the problems mentioned above, the Edge Attention Model (EAM)and the Edge Attention Net (EANet) were proposed by using Encoder-Decoder framework. In the encoder, the residual network ResNet34 pre-trained on ImageNet and the EAM were utilized, so as to fully obtain the detailed feature information of liver edge; in the decoder, the deconvolution operation and the proposed EAM were used to perform the feature extraction to the useful information, thereby obtaining the semantic segmentation diagram of liver image. Finally, the smoothing was performed to the segmentation images with a lot of noise. Comparison experiments with AHCNet were conducted on three datasets, and the results showed that:on 3Dircadb dataset, the Volumetric Overlap Error (VOE) and Relative Volume Difference (RVD) of EANet were decreased by 1.95 percentage points and 0.11 percentage points respectively, and the DICE accuracy was increased by 1.58 percentage points; on Sliver07 dataset, the VOE, Maximum Surface Distance (MSD) and Root Mean Square Surface Distance (RMSD) of EANet were decreased approximately by 1 percentage points, 3.3 mm and 0.2 mm respectively; on clinical MRI liver image dataset of a hospital, the VOE and RVD of EANet were decreased by 0.88 percentage points and 0.31 percentage points respectively, and the DICE accuracy was increased by 1.48 percentage points. Experimental results indicate that the proposed EANet has good segmentation effect of liver image.