In this paper a practical approach to design an optimal robust Power System Stabilizer (PSS) is presented which improves the PSS dynamic performance facing uncertainty in its model parameters. Generally, the PSS system is a critical element in increasing the damping of the system in an emergency condition and it is necessary to strengthen its dynamic characteristics against any uncertainty in its model parameters. To model the uncertainty in the PSS, it is decomposed into two matched and unmatched types of uncertain components. The linear quadratic regulator (LQR) problem is then used to handle the matched component, while an augmented control is used to manage the unmatched component. To evaluate the robustness of the proposed optimal robust PSS system, the IEEE PSS1A PSS system model considering the reported uncertainties in its model parameters is used.