To solve the forecasting problems of system behavior affected by driving factors with a complicated changing patterns, a driving foctor control grey model of N variables driving foctor control grey model of N variables(DFCGM$(1, N)$) model based on driving factors control and its derived model are designed by introducing a driver function into the construction of the grey action item in the conventional GM$(1,N)$ model, and subsequently the method of estimating the parameters is discussed. According to the sufficient and insufficient information about the driving factors, empirical analysis and intelligent optimization algorithms are used to explore the estimation of driving factors control parameters, respectively, and subsequently the modeling procedure is given with a flowchart. Finally, the effectiveness and practicality of the proposed model are verified by forecasting the grain production in China. Results show that the proposed model can effectively solve the forecasting problems on the system affected by multiple driving factors.