Summary: This article presents a fuzzy goal programming (FGP) procedure for modeling and solving multilevel programming (MLP) problems by using genetic algorithm (GA) in a large hierarchical decision making system. In the proposed approach, an GA scheme is introduced first for searching of solutions at different stages and thereby solving the problem and making decision in the order of hierarchy of execution of decision powers of the decision makers (DMs) located at different hierarchical levels. In the proposed GA scheme, Roulette-wheel selection scheme, single point crossover and random mutation are adopted to search a satisfactory solution in the hierarchical decision system. To illustrate the potential use of the approach, a numerical example is solved.