This paper presents a new approach and corresponding experiments for the nonlinear robust control of a superconducting magnetic energy storage (SMES) unit to improve the transient stability of power systems. Based on the result of SMES prototype experience, a new dynamic model with disturbances of SMES is adopted, and transferred to the per unit system for simplifying the dynamic analysis and controller design. Then, feedback linearization scheme and linear H-infinity control theory are applied to design a novel SMES nonlinear robust controller in a one-machine infinite bus (OMIB) power system. In order to confirm such positive effects of the proposed control strategy, experiments are carried on a laboratory setup of SMES comparing that with a conventional proportional-integral (PI) controller. The results of experiments demonstrate that the proposed nonlinear robust controller has more excellent performance to improve the transient stability of power systems than that of conventional PI controllers.