Accurate segmentation of liver is still a challenging problem due to its large shape variability and unclear boundaries. The purpose of this paper is to propose a neural network based liver segmentation algorithm and evaluate its performance on abdominal CT images. First, we develop a fully convolutional network (FCN) for volumetric image segmentation problem. To guide a neural network to accurately delineate the target liver object, we apply self-supervising scheme with respect to edge and contour responses. The deeply supervising method is also applied to our low-level features for further combining discriminative features in the higher feature dimensions. We used 160 abdominal CT images for training and validation. Quantitative evaluation of our proposed network is presented with 8-fold cross-validation. The result showed that our method successfully segmented liver more accurately than any other state-of-the-art methods without expanding or deepening the neural network. The proposed approach can be easily extended to other imaging protocols (e.g., MRI) or other target organ segmentation problems without any modifications of the framework.