This paper presents a hysteresis mathematical model of a shape memory alloy (SMA) actuator for feedforward hysteresis compensator. The hysteresis model represents the relation between temperature, stress, and electric resistance. Firstly, based on the laws of thermodynamics, the hysteresis model of the SMA actuator is built. Secondly, the inverse of the hysteresis model is obtained to produce a compensator for non‐linear characteristics such as hysteresis and saturation. Thirdly, the parameters of the hysteresis model are obtained from each experiment under constant load and constant temperature, and the model validity is confirmed by comparing experimentally obtained results. Finally, the inverse model is applied to a part of feedforward hysteresis compensator. In order to verify the effectiveness of the proposed model as hysteresis compensator, an electrical resistance control using feedback–feedforward control was conducted by numerical simulation. The simulation results indicate advantages of the proposed mathematical model in hysteresis compensation of SMA actuator, and demonstrate that the model is capable of handling load fluctuation.