The recursive relationship of the accumulative sequence is deduced according to the original sequence of non-homogeneous exponential of time response function of GM(1,1) model, and the direct estimation method is constructed to solve the parameters values of the time response function. Then, an NGM(1,1) model which can simulate approximate homogenous exponential sequence and approximate non-homogenous exponential sequence is proposed. This NGM(1,1) model avoids the jumping error of the model parameters estimation from difference equation to differential equation, and explains theoretically the reason for its capability of simulating the homogenous and non-homogenous exponential sequence. The results show that the simulation and prediction of the proposed model is more excellent through the comparison of the new NGM(1,1) and the existing models.