Aiming at solving the predicting problems for the decreasing non-homogenous series, the grey model NGOM(1,1) is proposed with the method of accumulated generating operation in opposite-direction. The parameters and time response function are estimated. For the background value and the initial condition have a great effect on the simulating and predicting accuracy of the grey model, the background value is optimized by using the equations, and the initial condition is modified by using the expectation function, which ensures the consistency between the two rules, namely, the minimum values of optimized objective function and the minimum average relative errors. The results of the case study show that the NGOM(1,1) model has better simulating accuracy compared to other optimized models, which demonstrates the effectiveness and practicability of the proposed model dealing with the decreasing non-homogeneous sequences.