The formula of background value is one of the main factors causing systematic error of GM(1,1) model. A construction method for optimizing GM(1,1) model is proposed. According to structure characteristics of GM(1,1) time response function, the mean value theorem of integral is used to fit the real background value, and the relationship between the background value and the development rate is analyzed. Then, a new grey differential equation is constructed, and the parameter vector is evaluated by using the least square method, and the original parameters are restored by equations system. The new background satisfies the unbiased property and least error. Finally, a numerical case shows that the proposed algorithm breaks the confine of modeling high growth sequences, and the application indicates that the optimized model has an obviously high accuracy in the actual problem.