Automatic 3D liver segmentation is a fundamental step in the liver disease diagnosis and surgery planning. This paper presents a novel fully automatic algorithm for 3D liver segmentation in clinical 3D computed tomography (CT) images. Based on image features, we propose a new Mahalanobis distance cost function using an active shape model (ASM). We call our method MD-ASM. Unlike the standard active shape model (ST-ASM), the proposed method introduces a new feature-constrained Mahalanobis distance cost function to measure the distance between the generated shape during the iterative step and the mean shape model. The proposed Mahalanobis distance function is learned from a public database of liver segmentation challenge (MICCAI-SLiver07). As a refinement step, we propose the use of a 3D graph-cut segmentation. Foreground and background labels are automatically selected using texture features of the learned Mahalanobis distance. Quantitatively, the proposed method is evaluated using two clinical 3D CT scan databases (MICCAI-SLiver07 and MIDAS). The evaluation of the MICCAI-SLiver07 database is obtained by the challenge organizers using five different metric scores. The experimental results demonstrate the availability of the proposed method by achieving an accurate liver segmentation compared to the state-of-the-art methods.