Abstract: The background value is an important factor affecting the precision of non-equidistant multivariable MGM(1,n) model. Based on index characteristic of grey model GM(1,1), the characteristic of integral, improving the constructing method of background value, the function with non-homogeneous exponential law was used to fit the accumulated sequence via three points to obtain the background value of non-equidistant multivariable MGRM(1,n) model, taking the mean relative error as objective function, taking the modified values of response function initial value, a new non-equidistant multivariable new information optimizing MGRM(1,n) model based on accumulated generating operation of reciprocal number and improving background value was put forward which was taken the mth component as the initialization. The proposed MGRM(1,n) model can be used in non-equal interval and equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.