In this paper, a kind of Shape Memory Alloy (SMA) model based on hysteretic nonlinear theory and data mining was developed and applied in vibration control on rotor system with SMA bearing. Nonlinear difference item was introduced to interpret the hysteretic phenomenon of SMA. Arctangent function was introduced to describe the variation of SMA stiffness with temperature. Based on above, all of possible items in the model were found and stepwise multiple regression method was applied in finding the final relationship among strain, stress and temperature. Finally the stability and the bifurcation characteristic of rotor system with SMA bearing were analyzed. The result of significance test shows that the effects of all of the items in the final model are remarkable, which means that the model can describe the strain-stress curves of SMA in different temperatures well. The new SMA model broadens the region of controlling temperature, admits the existence of control error, and is easy to be analyzed in theory, which is helpful to vibration control.