In order to reduce the modeling errors of the discrete grey prediction model and increase the stability of the solution,this paper presents the fractional-order reverse accumulative discrete grey forecasting model(FORA-DGM(1,1)model).The perturbation bounds of the model was analyzed through the matrix perturbation theory.And it is proved that the FORA-DGM(1,1)model has the smaller perturbation bounds of solution than traditional discrete grey forecasting model.Thus,it has good stability.Finally,the FORA-DGM(1,1)mode was applied to predict the SO2 emission from industrial sector in Shanghai city.The modeling results show that the simulation error and prediction error of FORA-DGM(1,1)mode was less than traditional discrete grey forecasting mode,especially in the prediction aspects.And it verified the validity and practicability of the FORA-DGM(1,1)mode.