Internal friction has been measured for an AgInYb Tsai-type icosahedral (i-) quasicrystal to investigate an energy-dissipation mechanism by phason relaxation, possibly operating in quasicrystals. A fairly large peak of the magnitude Q À1 % 0:022 was observed, which was shown to be of the thermally-activated relaxation type. The frequency factor and activation enthalpy were evaluated to be 10 20 s ¹1 and 2:6 Â 10 À19 J (1.6 eV), respectively. The observed peak was analyzed on the assumption that it is of phason-origin. The magnitude of the phonon-phason coupling constant was estimated to be 0:008® (®: shear modulus), based on the model of the phonon-phason elastodynamics previously proposed. This value is comparable to those previously reported for Mackay-type i-phases such as i-AlPdMn and i-AlCuFe.