From the observation that possible values of parameters involved in objective functions and constraints of mathematical programming problems are often only imprecisely or ambiguously known to experts, in this paper we consider two-level integer programming problems with fuzzy parameters represented by fuzzy numbers.A computational method based on Genetic algorithms for obtaining the Stackelberg solution to two-level linear programming problem with fuzzy parameters is developed. Computational experiments are carried out in order to demonstrate the efficiency of the proposed computational method.