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The construction method of background value has been researched in this paper because it is one key to affect the precision and adaptability of GM(1,1) model. And a new calculation formula of background value has been reestablished based on the literatures. Besides, in order to further improve the precision, the initial value of GM (1,1) prediction formula has been developed and optimized by using the minimum sum of error square. The fitting and predictive results of examples indicate that the new model has higher precision and is suitable for both low and high developing coefficient data sequence.