A novel scheme using H∞ optimal control theory to design a H∞ static VAr controller (SVC) for a static VAr system (SVS) connected at the generator bus is presented in this paper. The considered system is properly selected to be a typical one-machine infinite-bus power system to clearly demonstrate the effectiveness of the proposed H∞ SVC for damping enhancement of generator oscillations. For effectively stabilizing system oscillations, some key points of a H∞ controller design such as minimizing the effects of external disturbances, change of system operating conditions, and input of high-frequency noises, etc. are considered. The time-domain approach based on nonlinear model simulations under various disturbance conditions is carried out. The simulation results show that the proposed H∞ SVC incorporated with the SVS can effectively stabilize generator oscillations.