In this paper, it is suggested that the selection method of parameter of Power System Stabilizer(PSS) with robustness in low frequency oscillation for Static VAR Compensator(SVC) using a self tuning fuzzy controller for a synchronous generator excitation and SVC system. The proposed parameter self tuning algorithm of fuzzy controller is based on the steepest decent method using two direction vectors which make error between inference values of fuzzy controller and output values of the specially selected PSS reduce steepestly. Using input-output data pair obtained from PSS, the parameters in antecedent part and in consequent part of fuzzy inference rules are learned and tuned automatically using the proposed steepest decent method.