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In this paper we propose a new approximation algorithm for calculating the min-cut tree of an undirected edge-weighted graph. Our algorithm runs in O(V 2 .logV + V 2 .d), where V is the number of vertices in the given graph and d is the degree of the graph. It is a significant improvement over time complexities of existing solutions. However, because of an assumption it does not produce correct result for all sorts of graphs but for the dense graphs success rate is more than 90%. Moreover indoi:10.5120/12084-9170 fatcat:5q4t3kwukzgqdkelu47t7klzwi