To solve the modeling problem of the small sample system with interaction effects, the GM(1,N) model with interaction effects and its derived model are constructed by introducing cross terms into the grey acting term of the classical GM$(1,n)$ model. Thus the impacts of interaction effects between different input variables on systems' characteristic variables can be effectively reflected. An actual example is studied to illustrate the effectiveness of the GM(1,N) model with interaction effects. The results showthat the GM(1,N) model with interaction effects degenerate into the classical model when the interaction coefficients between related factors are zero. The model with interaction effects has higher simulation and prediction precision than that of classical model for the systems modeling problem with interaction effects.