In the situation of considering the decision-maker's risky attitude and psychological behavior, a decision analysis method based on the regret thoery is proposed to solve the problem of grey-stochastic multi–criteria decision-making in which the criteria value of alternatives and the probability are both grey numbers. Firstly, original criteria values are converted into standard grey numbers, and the standard grey risky decision matrix under various conditions is obtained by using the normative approach. Then, the grey perceived utility function is defined based on the regret thoery. A multi-objective optimization model which produces the maximum grey overall perceived utility values of alternatives is constrcted to get the optimum weight vector, so that the optimal grey perceived utility value of each scheme is ranked by the sorting rules of interval grey numbers. Finally, an example is provided to illustrate the practicability and effectiveness of the proposed method.