Temperature dependence of Ag-109, Ag-107, Ga-71 and Ga-69 NMR line shapes and relaxation times (T-1 and T-2) have been measured for the ionic conductor Ag9GaSe6. In the high temperature cubic phase (Phase I), which is known to show X-ray diffuse scattering, line widths of Ag-109 signals have suggested that the motional narrowing is completed. T-1 of the all nuclei increases with increasing temperature, and T-1 of Ag-109 and Ag-107 are independent of the magnetic field strength. The experimental T-1 ratio of Ag-107 to Ag-109 and the magnetic field independence of T-1 in the fast motion limit can be explained by the scalar coupling of first kind in terms of an exchange interaction. The temperature dependences of T-1 of mobile Ag and Ag-107 are weaker than those of immobile Ga-71 and Ga-69. Ga-71 and Ga-69 signals have shown that a new middle temperature phase (Phase II) exists in a narrow temperature range around 282 K. In this phase, Ag signals show the spectral width of 200 ppm. X-ray diffraction patterns have also shown diffuse scattering, and have been indexed on the basis of the trigonal lattice. In the low temperature cubic phase (Phase III), Ag signals have shown the chemical shift anisotropy width of which is about 1000 ppm.