Abstract: The basis of the grey forecasting model is the accumulation of original data. The rule of system change can be highlighted through the accumulation of data. The fractional-order accumulation discrete grey forecasting model presents a fractional-order accumulation method for raw data. The stability of the model can be effectively increased by fractional-order accumulation. The fractional-order reverse accumulation discrete grey forecasting model can make full use of the new information of the system, which is more consistent with the principle of new information priority. In this paper, the characteristics and advantages of the two models are compared theoretically and verified by an example. We found that when the old data of the original data were disturbed, the stability of the discrete grey forecasting model with reverse fractional-order accumulation was good.