Abstract: A method of stochastic multiattribute decision making was proposed where the attribute values were in form of stochastic variables. Describing and analyzing the ASD rules, the ASD degree was defined with its calculation formula given. Then, dominance relations on pairwise comparisons of alternatives were established according to ASD rules, thus ASD degrees of alternative pairs were calculated and the ASD degree matrix with regard to each attribute was built. Furthermore, total relative ASD degree of each alternative is calculated to obtain the ranking of alternatives. A numerical example is given to illustrate the feasibility and validity of the proposed method.