In this paper, we propose a new method to detect liver tumors in CT images automatically. The proposed method is composed of two steps. In the first step, tumor candidates are extracted by EM/MPM algorithm; which is used to cluster liver tissue. To cluster a dataset, EM/MPM algorithm exploits both intensity of voxels and labels of the neighboring voxels. It increases the accuracy of detection, with respect to other probabilistic approaches. In the second step, false positive candidates are filtered by using shape information. We use tumor shape information to reduce the false positive regions. As tumors have usually a sphere-like shape, we just need to check the circularity of the candidate regions in each slice to reject false positive. We also reject those candidate tumors that their centroids are near the liver boundary. Quantitative evaluation of our method shows that it can decrease false positive rate successfully without decreasing true positive rate, compared with other conventional methods.