This paper presents an intelligent model; named as free model, approach for a closed-loop system identification using input and output data and its application to design a power system stabilizer (PSS). The free model concept is introduced as an alternative intelligent system technique to design a controller for such dynamic system, which is complex, difficult to know, or unknown, with input and output data only, and it does not require the detail knowledge of mathematical model for the system. In the free model, the data used has incremental forms using backward difference operators. The parameters of the free model can be obtained by simultaneous perturbation stochastic approximation (SPSA) method. A linear transformation is introduced to convert the free model into a linear model so that a conventional linear controller design method can be applied. In this paper, the feasibility of the proposed method is demonstrated in a one-machine infinite bus power system. The linear quadratic regulator (LQR) method is applied to the free model to design a PSS for the system, and compared with the conventional PSS. The proposed SPSA-based LQR controller is robust in different loading conditions and system failures such as the outage of a major transmission line or a three phase to ground fault which causes the change of the system structure.