In this paper, a novel discrete grey DGM (1,1,k,k²) model with time power term is presented, and the prediction formula is deduced, the parameter estimation method is given, and the initial value is optimized. This is a further extension after the discrete DGM(1,1) model, DGM(1,1,k) model and DGM(1,1,kα) model. Finally, the model has been applied to predict cumulative oil production, and good simulation and prediction results have been achieved, which shows that the model is reliable.