In the classical multivariate prediction model, most research studies focused on the selection of relevant behaviour factors and the stability of historical data for improving the predicting accuracy of the main behaviour factor, and the historical data of the main behaviour factor have never been considered as one relevant behaviour factor, which in fact can be the first key impact factor; besides, the historical data can directly predict the main behaviour in the time series forecasting model, such as the ARIMA model. In this paper, one modified MLR model combined with time series forecasting theory is presented and applied in grain consumption forecasting. In the proposed model, to improve the current grain consumption forecasting, how to select impact factors is also discussed by combining the grey relational degree and Pearson correlation coefficient with given weights, and the optimal preprocessing parameter by the moving average filtering is computed for eliminating the abnormal points and stabilizing the data. Finally, the selected main impact factors are inputted to the proposed modified MLR model for forecasting grain consumption. Simulation results have shown that the five-year mean absolute percentage error of ration and feed grain is 2.34% and 3.27%, respectively, and the prediction accuracy has improved up to 2 times compared with the BP model and LSTM model. Moreover, the robustness of the model is verified by prediction analysis at different time intervals of historical data.