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.