Most smart material based actuators (smart actuators) are known for their prominent characteristics of high resolution of positioning, high bandwidth, and the ease of integration in miniaturized systems. However, their applications are restricted by the inherent hysteresis nonlinearity. This paper presents a new modified Bouc-Wen (MBW) model which has a rate-dependent. property. Then the proposed model is directly used in developing a robust adaptive control in order to eliminate the hysteresis effects. Finally, the efficacy of the designed control framework is verified via a real case where a giant magnetostrictive actuator (GMA) is used as the testbed.