An attempt to solve fuzzy constraint satisfaction problems (FCSPs) with the use of genetic algorithms (GAs) is presented in the paper. A fuzzy relation that represents the degrees of satisfaction of fuzzy constraints in a given FCSP is considered as an objective function of the respective unconstrained optimization problem. A solution of a FCSP such that all constraints are satisfied to the maximal degree is searched for with a GA using the objective function to evaluate the prospective solutions with respect to fuzzy constraint satisfaction. The presented approach is illustrated with an example of a FCSP taking into account different levels of fuzzy granulation influencing GA's performance.