The modelling of electric power systems on the state space and an optimal control system known as Linear Quadratic Regulator (LQR) for designing the load frequency control system are realized in this paper. In order to obtain high quality electric energy on electric power systems, the fluctuations on voltage and frequency must be decreased as much as possible. The frequency sensitivity of the system must be reduced to minimum level against to load changes. To obtain minimum frequency sensitivity against to load changes, an optimal control known as Linear Quadratic Regulator ( LQR) is designed. In the study, the simplified and block diagram of the electric power system is employed. By using this diagram, the state equations for the power system are obtained on the state space. In the load frequency control of power system, control system via pole-placement and optimal LQR control method known as modern control with high reability rate are used. The proposed optimal LQR load frequency has been compared with control system via pole-placement. Load frequency control system of electric power system has been developed designed by using MATLAB/SIMULINK.