In order to describe the power asymmetry phenomenon in conflicts, facilitate power asymmetry conflict solving process and develop the asymmetric power analysis model of a decision making support system, based on the existing research framework of a conflict analysis graph model, this paper systematically expands the theory of the power asymmetry module. Firstly, the modeling elements of the graph model for concept solution are redefined using matrix theory, and the modified power preference matrix and power reachable matrix are given. Then, based on the previous study, in order to promote stability calculation under asymmetric power, five algebraic expressions of stability with the influence of power are defined. Finally, the asymmetric power stability analysis method is applied to solve a medical insurance conflict, and the resolve project is presented by means of stable solution. The results show that the proposed approach can effectively and accurately solve the conflicts of power asymmetry.