The hysteresis nonlinearity of the Magnetic Shape Memory Alloy (MSMA) actuator limits its control applications. To tackle the problems, usually the hysteresis behavior of these materials is models. Prandtl-Ishlinskii (PI) model is more practical in this area, because of its simplicity and having analytical inverse. Two versions of this model, entitled: rate-independent model and rate-dependent model, have been developed. Experimental results show that with increasing input frequency, the shape of hysteresis loops is amplified. In this study, by using experimental test setup the input voltage is applied to the MSMA actuator at the frequencies 0.05- 0.4 Hz and the displacement output captured by proximity position sensor, also the MSMA is modeled by generalized rate-dependent Prandtl-Ishlinskii (GRDPI) model and modified generalized rate-dependent Prandtl-Ishlinskii (MGRDPI) model. The modified version of the model are presented by the authors to enhance the ability of the GRDPI model for describing the asymmetric and saturated hysteresis behavior in MSMAs by hyperbolic tangent function in the model output. For training of the mentioned models, the actuation frequencies 0.05 and 0.2 Hz are selected and the model parameters of each model are also obtained by using genetic algorithm (GA). For validation of the models the hysteresis loop at frequency 0.1, 0.3 and 0.4 Hz is selected. The result shows that, due to using hyperbolic tangent function in the model output, the modified version of the GRDPI model can describe the hysteresis behavior in MSMAs more accurately.