With respect to the problem of multiple attribute decision making, in which attribute weights are unknown and attribute values are given in terms of normal triangular fuzzy stochastic variables, an approach for normal triangular fuzzy stochastic multi-attribute decision making is proposed based on the prospect mean-variance rule. Firstly, a normal triangular fuzzy stochastic decision matrix is constructed. A mean-variance decision matrix is then obtained by calculating the expectation and variance of the normal triangular fuzzy stochastic decision matrix. Secondly, a prospect effect is defined, and a prospect mean-variance matrix is built by setting an attribute reference point of each alternative. Moreover, an improved grey system theory model is built to determine the attribute weights. The prospect mean-value matrix is transformed into a comprehensive prospect mean-variance matrix. Finally, according to the prospect order relation defined, a ranking of alternatives is obtained. A practical example is given to show the feasibility and effectiveness of the proposed approach.