A new proposed method of fully automatic processing frameworks is based on graph-cut active contour algorithms. This paper addresses the problem of segmenting a liver and tumor regions from the abdominal CT images. A predicate is defined for measuring the evidence for a boundary between two regions using a Graph-based representation of the image. The algorithm is applied to image segmentation using two different kinds of local neighborhoods in constructing the graph. Liver and Hepatic Tumor Segmentation can be automatically processed by the graph-cut based method. This system has concentrated on finding a fast and interactive segmentation method for liver and tumor segmentation. In preprocessing stage, the CT image process with mean shift filter and statistical thresholding method for reducing processing area with improving detections rate. Second stage is liver segmentation; the liver region has been segmented using the algorithm of the proposed method. The next stage tumor segmentation also followed the same steps. Finally the liver and tumor regions are separately segmented from the computer tomography image.