Discretization is an effective tactic to improve the accuracy of grey prediction model. In order to further improve the accuracy of the discrete grey prediction model, based on the discrete grey DGMP(1,1,N) model with polynomial, the degree of polynomial is expanded from integer to fraction, and the discrete grey DGMFP(1,1,r) model with fractional polynomial is proposed in the present study. To determine the best DGMFP(1,1,r) model, the mean absolute percentage error (MAPE) is established as an objective function of the optimization model, and a quantum genetic algorithm is used to calculate the optimal degree of fractional polynomials in DGMFP(1,1,r) model. Finally, the empirical results from two application cases indicate that, compared with other discrete grey models, DGMFP(1,1,r) model has a higher simulation and prediction accuracy and can overcome the restrictions of DGMP(1,1,N) model class ratio test, and has stronger generalization ability and wider adaptability