Based on the idea of damping accumulated generation operator and discrete grey prediction model, a new damping accumulated discrete GM (1,1) (DADGM(1,1)) model is proposed. The specific process of the new model is derived. The relationship between the DADGM(1,1) model and the GM(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 by using the quantum particle swarm optimization algorithm. Finally, two practical examples are given. Numerical results show that the new proposed DADGM(1,1) model has better fitting and prediction efficiency than the above benchmark models.