This paper presents an optimal fuzzy power system stabilizer to damp out low frequency oscillation. So far fuzzy controllers have been applied to power system stabilizing controllers due to its excellent properties on the nonlinear systems. But the design process of fuzzy logic power system stabilizer requires empirical and heuristic knowledge of human experts as well as many trial-and-errors in general. This paper presents and optimal design method of the fuzzy logic stabilizer using the genetic algorithm. Non-symmetric membership functions are optimally tuned over an evaluation function. The present inputs of fuzzy stabilizer are torque angle error and the change of torque angle error without loss of generality. The coding method used in this paper is concatenated binary mapping. Each linguistic fuzzy variable, defined as the peak of a membership function, is assigned by the mapping from a minimum value to a maximum value using eight bits. The tournament selection and the elitism are used to keep the worthy individuals in the next generation. The proposed system is applied to the one-machine infinite-bus model of a power system, and the results showed a promising possibility.