In order to describe the hysteresis of magnetostrictive and piezoelectric materials and establisha high-precision feedforward compensation system, the prediction method of Preisach model’s first order reversal curve is studied.Firstly, the fundamental theorem of the first order reversal curve and the classical interpolation method is introduced. The deficiency of the linear classical interpolation method in the prediction of the first order reversal curve is pointed out.Then, based on the idea of nonlinear transformation, an auxiliary line method is proposed to predict the first order reversal curve.Finally, experiments are carried out to predict the first order hysteresis curves with auxiliary line method and classical interpolation method in giant magnetostrictive material (GMM) and piezoelectric ceramic transducer(PZT).In the case of GMM hysteresis, for any first order reversal curve, the root mean square error (RMSE) of the auxiliary line method is reduced to 14.22% of the RMSE of the classical interpolation methodat most. For all prediction data, the RMSE of the auxiliary line method is reduced to 29.42% of the RMSE of classical interpolation method.In the case of PZT hysteresis, for any first order reversal curve, the RMSE of the auxiliary line method is reduced to 18.18％ of the RMSE of the classical interpolation method at most. For all prediction data, the RMSE of the auxiliary line method is reduced to 41.07％ of the RMSE of classical interpolation method.The prediction accuracy of the auxiliary line methodis higher than the classical interpolation method. And the bigger the nonlinear error of the hysteresis is, the more the accurate of the auxiliary line method will be compared with the classical interpolation method.