Temperature dependence of Ag-109 NMR spectrum and spin-lattice relaxation T, was measured for a single crystal of Ag beta-alumina (Ag1.17Al11O17.09) at external magnetic field of 4.7 T (9.3 MHz) and 9.4 T (18.6 MHz). Only a single spectrum peak is observed at room temperature, it reflects fast site exchange of Ag ions. The chemical shift of the peak position depends on the angle between c-axis and external field B-o. From the angle dependence, the values of screening tensor are determined to be, sigma(PAS)(xx) = sigma(PAS)(yy) = sigma(PAS)(zz) = -212 ppm. The large difference between sigma(PAS)(zz) and sigma(PAS)(xx) indicates a strong interaction between Ag and surrounding oxygen. The relaxation mechanism is discussed using the Scalar Coupling (SC) model and Screening Tensor Fluctuation (STF) model. The field dependence of the T-1 observed at 4.7 T and 9.4 T strongly supports the SC model. It suggests that there are strong correlations between Ag ions in beta-alumina and it probably plays an important role to the high ionic conductivity. (C) 2008 Elsevier B.V. All rights reserved.