The aim of this paper is to suggest a design method of the optimal multivariable $H_{infty}$ control system using genetic algorithm (GA). This $H_{infty}$ control system is designed by applying GA to the optimal determination of weighting functions and design parameter $gamma$ that are given by Glover-Doyle algorithm which can design $H_{infty}$ controller in the state space. The first method to do this is that the gains of weighting functions and $gamma$ are optimized simultaneously by GA with tournament method. And the second method is that not only the gains and $gamma$ but also the dynamics of weighting functions are optimized at the same time by eA with roulette-wheel method. The effectiveness of this $H_{infty}$ control system is verified by computer simulation.