This paper deals with a systematic approach to GA-PI controller design for static VAR compensator(SVC) using genetic algorithms(GAs) which are search algorithms based on the mechanics of natural of natural selection and natural genetics, to improve system stability. A SVC, one of the Flexible AC Transmission System(FACTS), constructed by a fixed capacitor(FC) and a thyristor controlled reactor(TCR), is designed and implemented to improve the damping of a synchronous generator, as well as controlling the system voltage. To verify the robustness of the proposed method, considered dynamic response of generator used deviation and generator terminal voltage by applying a power fluctuation and three-phase fault at heavy load, normal load and light load. Thus, we proved usefulness of GA-PI controller design to improve the stability of single machine-infinite bus with SVC system.