The traditional grey models with two-parameters are always accompanied by the effect of extreme values in the raw sequence, which influences the accuracy of the simulation and prediction by grey models. This paper proposes a TPBVGM(1,1) model(three-parameters background values of the grey model with a single variable and a first order equation)by increasing the number of parameters in the background value. This novel model improves the smoothness of the background value and weakens the effects of extreme values in the raw sequence on the basis of proving that a two-parameter background value assignment is not reasonable. The objective of devising this model is to improve the accuracy of predictions. The TPBVGM(1,1) model is then applied to simulate and forecast the average water usage per person in the cities and towns along the Yangtze River basin; the simulation and prediction performance of the TPBVGM(1,1) model are then tested by comparison with the simulation and prediction results of traditional grey prediction models. The results show that the TPBVGM(1,1) model has a higher accuracy for simulation and prediction than the traditional grey prediction models. The results of the study provide a new research method for simulation and prediction with a grey system model.