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The robust H∞ control problem is addressed for a single machine infinite bus system with static var compensator (SVC), the damping coefficient uncertainty and external disturbances in this paper. Storage functions of the control system are constructed based on modified adaptive backstepping sliding mode control and Lyapunov methods. A nonlinear robust H∞ controller and a parameter updating law are obtained simultaneously. The controller cannot only attenuate the influences of external disturbances on the system output, but also has strong robustness for system parameters variations. Since the controller design is based completely on the nonlinear dynamic system without any linearization, the nonlinear property of the dynamic system is well preserved. The simulation results show that more rapid speed response and stronger robustness can be obtained by the proposed method than the conventional adaptive backstepping and adaptive backstepping sliding mode control methods.