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 zero-one programming problems with fuzzy parameters represented by fuzzy numbers. Using genetic algorithms, we present a computational method for obtaining Stackelberg solutions to the two-level zero-one programming problem with fuzzy parameters. To demonstrate feasibility of the method,computational experiments are carried out.