Segmentation of liver in abdominal computed tomography (CT) is an important step for radiation therapy planning of hepatocellular carcinoma. Practically, a fully automatic segmentation of liver remains challenging because of low soft tissue contrast between liver and its surrounding organs, and its highly deformable shape. The purpose of this work is to develop a novel superpixel-based and boundary sensitive convolutional neural network (SBBS-CNN) pipeline for automated liver segmentation. The entire CT images were first partitioned into superpixel regions, where nearby pixels with similar CT number were aggregated. Secondly, we converted the conventional binary segmentation into a multinomial classification by labeling the superpixels into three classes: interior liver, liver boundary, and non-liver background. By doing this, the boundary region of the liver was explicitly identified and highlighted for the subsequent classification. Thirdly, we computed an entropy-based saliency map for each CT volume, and leveraged this map to guide the sampling of image patches over the superpixels. In this way, more patches were extracted from informative regions (e.g. the liver boundary with irregular changes) and fewer patches were extracted from homogeneous regions. Finally, deep CNN pipeline was built and trained to predict the probability map of the liver boundary. We tested the proposed algorithm in a cohort of 100 patients. With 10-fold cross validation, the SBBS-CNN achieved mean Dice similarity coefficients of 97.31 ± 0.36% and average symmetric surface distance of 1.77 ± 0.49 mm. Moreover, it showed superior performance in comparison with state-of-art methods, including U-Net, pixel-based CNN, active contour, level-sets and graph-cut algorithms. SBBS-CNN provides an accurate and effective tool for automated liver segmentation. It is also envisioned that the proposed framework is directly applicable in other medical image segmentation scenarios.