Based on the idea of damping accumulated generation operators and discrete grey prediction models, a new damping accumulated discrete GM(1,1) (DADGM(1,1)) model is proposed, and its specific process is derived. The relationship between theGM(1,1) model, the discrete GM(1,1) model, the damping accumulated GM(1,1) model is theoretically analyzed. Stability property and the analysis of data application types of the DADGM(1,1) model are discussed, and the optimal damping accumulative parameter is searched using the quantum particle swarm optimization algorithm. Finally, two practical examples are given. Numerical results show that the proposed DADGM(1,1) model has better fitting and prediction efficiency than the above benchmark models.