Abstract.We have carried out inelastic x-ray scattering measurements on liquid water-glycerol mixtures. The data are analyzed by a damped harmonic oscillator model with two excitations, longitudinal and transverse modes. The sound velocity of the longitudinal mode is almost constant (about 3.1 km/s), being independent of the composition. Thus the strength of 'fast sound' which we define the ratio of this IXS sound velocity to ultrasonic one is largest at pure water and gradually decrease with increasing mole fraction of glycerol. This result indicates that the relaxation phenomena of pure water gradually reduce with increasing the fraction of the solute: the scenario which we proposed for water-monohydric alcohol mixtures hold true for this water-trihydric alcohol mixtures.