This study of QENS analysis has been undertaken on a N a − β′′ − alumina. Two incident energies, 1.95 meV and 3.55 meV have been used in a range of -1.5,+1.5 and -2,+2 and data were collected at 140K and 400K. Two components have been found by fitting the data with Lorentzian model. It has been observed that a broader component corresponds to fast diffusion because of the presence of large number of vacancies in the structure, while, a narrow component shows a slower and more localized jumps. The wider compo- nent displayed a Q-dependence which suggest that the Q.E signal is mainly because of long range diffusion of N a+, while the narrow width component showed Q-independence. A Chudley-Elliot model has been utilized using residence time of 1 ps and jump length of 3 Å. The agreement has been observed between the broader width parameters over Q and the model, which verified that N a+ exhibits jump diffusion.