Abstract: A novel method for liver tumor CT image auto-segmentation is proposed in this paper.By utilizing minimal spanning tree of graph, the method can search for homogeneous region of image, and image segmentation can be conducted in time with union by rank and path compression.The method is evaluated via 52 liver tumor CT images, the results demonstrate that average minimum euclidean distance (AMED) and area overlap measure are 8.7540 and 95.15% respectively, and segmentation accuracy is optimal.These results show that the proposed method can auto-segment liver tumor quickly and precisely.