The parameter estimation error of the traditional grey NGM(1, 1, k) model is an important factor that leads to the instability of the model. It is an important method to improve the performance of the grey model by studying the parameter estimation method based on the background value optimization. Firstly, the grey differential equation, which matches with the winterization equation of the NGM(1, 1, k) model, is obtained by integral transformation, and the formula to optimize the background value of this model is deduced. Then the grey NGM(1, 1, k) model based on the optimized background value is constructed, and it is proved theoretically that the novel model can simulate the homogenous and non-homogenous exponential sequences simultaneously. Finally, the simulation and prediction accuracy of the proposed model are verified by a numerical example and an application example respectively.