A relative superioritybased alternatives ranking method is proposed to solve the type of multiattribute risk decision making problem. The comparison between two alternatives derives from the jointly function of prospects' gains/losses and risk, so the information entropy and standard deviation are introduced and taken as the risk measurements for the prospect, then the concept of relative superiority based on the difference of expected utility and risk measurements between the two alternatives is proposed to depict the relative superiority degree. And the weight vector and preference rank of all the alternatives can surface from the matrix of comprehensively relative superiority. The cases show that the proposed method is effective.