Segmentation of liver from CT scans is essential in computer-aided liver disease diagnosis and treatment. However, the 2DCNN ignores the 3D context, and the 3DCNN suffers from numerous learnable parameters and high computational cost. In order to overcome this limitation, we propose an Attentive Context-Enhanced Network (AC-E Network) consisting of 1) an attentive context encoding module (ACEM) that can be integrated into the 2D backbone to extract 3D context without a sharp increase in the number of learnable parameters; 2) a dual segmentation branch including complemental loss making the network attend to both the liver region and boundary so that getting the segmented liver surface with high accuracy. Extensive experiments on the LiTS and the 3D-IRCADb datasets demonstrate that our method outperforms existing approaches and is competitive to the state-of-the-art 2D-3D hybrid method on the equilibrium of the segmentation precision and the number of model parameters.