The diffusional motion of mobile Ag ions was studied by molecular dynamics (MD) simulation in the super ionic conductor Ag beta-alumina. The diffusion coefficient of Ag ion was estimated from the mean square displacement and the velocity correlation function, especially from the cross-correlation among the Ag ions. The velocity auto-correlation and cross-correlation functions exhibited approximately similar contribution to the Ag ionic diffusion at 300 K. The result of cross-correlation occurring cooperative ionic motion provided a qualitative explanation for the super ionic conduction.