Using limited data to predict the development trend is a widespread problem in the field of data modeling. When dealing with such problems, a grey prediction model faces the challenge of adapting to the irregular fluctuation characteristics of data. Based on the grey prediction model, this paper proposes a rolling modeling method that dynamically adapts to the data characteristics, and establishes the AGRM(1,1) model combined with the full information variable weight buffer operator that contains two parameters. The model uses the unbiased optimized grey prediction model to accurately simulate different growth coefficients on the basis of data slicing, and uses the buffer operator chain to adjust the data. Finally, an operator parameter optimization method based on the differential evolution algorithm is designed. The model changes the monotonous structure of the form of the traditional grey prediction model's time response function, and realizes the accurate prediction of the sequence with fluctuation and oscillation. In the case study, the test data of different growth coefficients are used to verify that the {AGRM(1,1)