The aim of this paper is to suggest a design method of the optimal model following control system using gerelic algoritlun (GA). This control system is designed by applying GA with reference model to the optimal determinination of weighting matrices Q, R that are given by LQ regulator prooblem. The method to do this is that all the diagooal elements of weighting matrices are optimized simultaneously by GA, in the search domain selected adequately. And, we design the mxiel following control system to boiler-turbine equipment by the proposed mothod. The model following control system designed by this mothod has the better command tracking perfannaoce than that of the control system designed by the trial-and-error method. The effectiveness of this cootrol System is verified by computer simulation.