Abstract: Based on the basic principle of information overlap in the grey system,this paper educes the estimate arithmetic of parameter α in GM(1,1) power model.The influence of various values of parameter α on the character of model solution is discussed.Simultaneously the paper renews the theorem of the solution to whitenization differential equation and presents two methods to optimize the model solution.The result shows that the modeling method proposed here is more suitable for fluctuating sequences that has a saturated condition or whose development is affected by multitudinous factors.When 0<α<1 and a>0 or α>1 and a<0,two models,GM(1,1) power model and grey Verhulst model,have the same limit properties but the GM(1,1) power model has superiority over the Verhulst model in the aspects of applicable scope and forecast precision.