Research on graph model for conflict resolution with consistent preference is carried out in this paper to depict complicated behaviors of decision makers in real conflicts and improve the stability drawback of the graph model for conflict resolution.Firstly, the preference of a decision maker is divided into consistent preference and inconsistent preference to show more important and accurate information about the conflict for the decision maker.Then the four basic stability concepts are expanded to eight stability concepts with consistent preference which can not only reflect the decision behaviors of the win-win, selfish and hybrid decision makers, but also effectively predict the equilibrium results of the aforementioned three types of decision makers.Finally, this method is applied to enterprise pollution dispute to demonstrate its effectiveness.