The polynomial time-varying parameters discrete grey prediction model(PDGM (1,1,m) model) is a novel method to deal with the system that contains both exponential and polynomial trend. The PDGM (1,1,m) model can provide satisfactory modeling accuracy for a stable system. However, high-order PDGM (1,1,m) models are prone to overfitting and the prediction error increases significantly. Therefore the fractional order cumulative polynomial time-varying parameters discrete grey prediction model (FPDGM (1,1,r) model) is proposed in this paper. It is found that the perturbation bounds of the FPDGM (1,1,r) model are smaller than that of the PDGM (1,1,m) model by using the matrix disturbance theory. And the overfitting problem can be reduced well by the FPDGM (1,1,r) model. Finally, numerical example and actual cases show that the accuracy of the new model is higher than that of the traditional grey model. The practicability and validity of the model are further verified.