GM(1,1) model is widely applied in the uncertainty prediction of less data and poor information, but it is often limited in true application because it is established with equal interval, then the grey prediction model with unequal interval performs a more important realistic function. Currently, the traditional unequal interval grey model (UGM(1,1)) and its amendatory model are established based on exponential model, which could not fit on linear series prediction. In order to overcome the drawbacks of the traditional unequal interval grey model (UGM(1,1)) and its amendatory model, a new amendatory unequal interval grey model (AUGM(1,1)) is proposed by adding linear ingredient and adopting the metabolism theory. The result of simulation and the comparative analysis show that the amendatory model is better than the UGM(1,1) model in accuracy and practicality, and overcomes the shortage that the traditional one could not be used in linear series, in this way, the application field of the grey model is expanded.