The longitudinal acoustic mode propagating along the three-fold z axis in NaNO3 has been studied by Brillouin scattering in the temperature range between 23.22 degrees C and 299.55 degrees C. The frequency shift and the spectral width of the Brillouin peak show anomalous behavior near the transition temperature T-c = 276.5 degrees C. The relaxation time of the antiferrodistortive mode of NO, ions is calculated from these anomalies through the use of Debye type susceptibility. The temperature dependence of the relaxation time has been determined below T-c to be tau(f)/(T-c - T), where tau(f) is (6.0 +/- 0.7) x 10-(11) sec deg.