This paper suggests a deign method of the model-following $H{infty}$ control system having robust performance. This $H{infty}$ control system is designed by applying genetic algorithm(GA) with reference model to the optimal determination of weighting functions and design parameter ${gamma}$ that are given by $H{infty}$ control theory. These weighting functions and design parameter ${gamma}$ are optimized simultaneously in the search domain guaranteeing the robust performance of closed-loop system. The effectiveness of this $H_{infty}$ control system is verified by computer simulation.