Ionic conductivity and alkaline stability are the key properties that limited the widespread application of anion-exchange membranes (AEM) in electrochemical energy conversion/storage systems. In recent years, quaternary ammonium functionalized poly (ether ether ketone) (PEEK) membranes serve as a promising solution due to the good mechanical and chemical properties. Varied ionic conductivity and alkaline stability could be obtained when the membrane contains different functionalized side chains. However, it's still a challenge to understand the mechanism from the experimental study because various parameters could affect the electro-chemical performance of the membranes. In this work, we conduct coarse-grained molecular dynamics simulations to investigate two PEEK-based membranes, in which the side chains contain one (SQ) or two (GQ) quaternary ammonium groups. The simulation results indicate the self-diffusion coefficients in SQ and GQ are quite similar which should not be the main reason for the improved ionic conductivity of GQ, while the obviously increased ion-exchange capacity of GQ should result in the improved ionic conductivity. Furthermore, the simulation reveals that more water molecules wrap around the OH− in GQ, which could lead to the improved alkaline stability in comparison to that of SQ. This work provides a deeper understanding for the design of grafted copolymer based AEM with QA functional side chains. Display omitted •Coarse-grained molecular dynamics simulations of the SQ and GQ AEMs were conducted.•The ions diffusion has little contribution to the improved ionic conductivity of GQ.•The improved ionic conductivity should attribute to the obvious promotion of IECs.•More H2O molecules wrap around OH− in GQ, leading to the better alkaline stability.