Abstract：A cubic time-varying parameters discrete grey forecasting model(referred to as CDGM(1, 1)) is constructed by introducing cubic time-varying terms, whose properties are studied. It is concluded that the CDGM(1, 1) possesses white exponential law coincidence, linear law coincidence, quadratic law coincidence, cubic law coincidence and consistency of stretching transformation. Furthermore, the optimization method is applied to optimize the iterative starting value of the proposed model, and the steps of using CDGM(1, 1) are introduced to predict. Finally, the proposed model is compared with another two discrete grey models through an instance. The results show the proposed model greatly improves the simulation and prediction precision.