In the paper, a quadratic term is added on the basis of NGM (1,1,k) model, so that it can be applied to the case where the incremental sequence of the original sequence is a non-homogeneous exponential sequence, and it researches from the optimum of grey derivative. Firstly, the k of accumulative sequence should be continued into t and then deviate t, the value of the derivative function act as the value of grey derivative. Thus, a GM(1,1) model suitable for homogeneous and non-homogeneous exponential growth sequences is established. The method of solving parameters is given; also the simulated prediction formula is selected to substitute the initial condition for undetermined parameters C . It is proved theoretically that the optimized model has coincidence of albino coefficient, exponent and translation constant. Finally, an example is given to demonstrate that the model can not only completely fit the strict non-homogeneous exponential sequence, but also it has higher simulation accuracy for near non-homogeneous exponential series.