In this paper we proposed a new approximation algorithm for calculating the min-cut tree of an undirected edge-weighted graph. Our algorithm runs in O (V2.logV + V2.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. We implemented our algorithm in objected oriented programming language and checked for many input cases. 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 in the unsuccessful cases, the deviation from actual result is very less and for most of the pairs we obtain correct values of max-flow.