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As to the applied range and optimization of grey forecast model, according to the principle that grey GM(1,1) model's parameters are grey and adjustable, the connotation model and parameter packet formulas of GM(1,1, β) were put forward in this paper, and some properties of the model and model's optimization algorithm was analyzed. The results show that the objective valuing region of parameter a of GM(1,1, β) model is (-∞+ ∞), and the objective valuing region of parameter a of GM(1,1) model is (- 2,+2), the objective valuing region of parameter a is determined by the background value coefficient, and it has nothing with raw data sequence; GM(1,1, β) grey differential equation completely suits for the homogeneous exponential function series. Finally, the example of simulating and forecasting the per capita income of urban dwellers in China shows that the grey differential equation GM(1,1, β) is valid. [ABSTRACT FROM AUTHOR]