The common models used for grey system predictions include the GM(1, 1), the GM(N, 1), the GM(1, N) and so on, in which the GM(N, 1) model is an important type. Especially, the GM(2, 1) model is used widely, but it shows low modeling precision sometimes because of the improper parameter estimation method. To improve the model's precision, the paper proposes an extended grey GM(2, 1) model and gives a new parameter estimation method for the extended GM(2, 1) model based on the difference equation. The paper builds eight different grey models for the example. Results show that the improved method proposed has the highest precision. The method proposed can improve the popularization and application of the grey GM(N, 1) model.