Summary: In this paper, the modeling and prediction problem of non-negative decreasing sequence are considered. Considering that a grey action will develop and change with the change of time and space, the grey action is approximately regarded as a linear function of time to construct a \(\text{GOM} (1, 1)\) model with grey action optimization. The optimal background value of \(\text{GOM} (1, 1)\) model is derived by integration based on the non-homogeneous exponential characteristics of the data series of the grey prediction model. Based on the principle of minimum square sum of mean relative error between an original sequence and a simulated sequence, the optimal time response function expression is determined, and the improved algorithm of complete \(\text{GOM} (1, 1)\) model is finally formed. Finally, the effectiveness and practicability of the improved model are verified by an application example.