To solve the problems that the traditional GM(1,N) model can not describe precisely the changing patterns of the system behavior characteristic variables influenced by the dummy variables in the real life, the dummy variables are introduced into the grey acting term of the conventional GM(1,N) model, and the novel GM(1,N) model is built with discussing the estimating methods of the parameters. Due to the great effect of the background value on the precision of modeling, the interpolated coefficient of the background value is optimized by using the PSO algorithm. The test methods of validity are proposed from two perspectives. Finally, the per capital income of farmers in Henan province is simulated and predicted, which shows that the proposed model can effectively describes the future trend of system change influenced by dummy variables.