Abstract: The error of GM (1，1) model is mainly from the background value and the initial value， thus the paper puts forward three different construction methods of background value， viz. the method of changing fixed right of background value to the variable right， the method of abstracting the data sequence as index function to construct background value， the method of abstracting the data sequence non homogeneous exponential function to construct background value. And the prediction accuracy of the three methods for background value were compared by setting up GM (1， 1) model with the initial value of X (n). Because the prediction accuracy of future development model for GM (1，1) model is weak， we use metabolism way to establish GM (1， 1) model and continuously optimize and update the model to avoid the large error. The prediction accuracy of GM(1，1) model from the three different construction methods of background value was compared with the engineering examples. The results show that the method of abstracting data sequence as non homogeneous exponential function has a higher prediction precision， and it can provide reference for similar projects.

Key words: GM(1, 1) model, background value, metabolic method, prediction precision