Natural gas hydrate is a new clean energy source in the 21st century, which has become a research point of the exploration and development technology. Acoustic well logs are one of the most important assets in gas hydrate studies. In this paper, an improved Carcione−Leclaire model is proposed by introducing the expressions of frame bulk modulus, shear modulus and friction coefficient between solid phases. On this basis, the sensitivities of the velocities and attenuations of the first kind of compressional (P1) and shear (S1) waves to relevant physical parameters are explored. In particular, we perform numerical modeling to investigate the effects of frequency, gas hydrate saturation and clay on the phase velocities and attenuations of the above five waves. The analyses demonstrate that, the velocities and attenuations of P1 and S1 are more sensitive to gas hydrate saturation than other parameters. The larger the gas hydrate saturation, the more reliable P1 velocity. Besides, the attenuations of P1 and S1 are more sensitive than velocity to gas hydrate saturation. Further, P1 and S1 are almost nondispersive while their phase velocities increase with the increase of gas hydrate saturation. The second compressional (P2) and shear (S2) waves and the third kind of compressional wave (P3) are dispersive in the seismic band, and the attenuations of them are significant. Moreover, in the case of clay in the solid grain frame, gas hydrate-bearing sediments exhibit lower P1 and S1 velocities. Clay decreases the attenuation of P1, and the attenuations of S1, P2, S2 and P3 exhibit little effect on clay content. We compared the velocity of P1 predicted by the model with the well log data from the Ocean Drilling Program (ODP) Leg 164 Site 995B to verify the applicability of the model. The results of the model agree well with the well log data. Finally, we estimate the hydrate layer at ODP Leg 204 Site 1247B is about 100−130 m below the seafloor, the saturation is between 0−27%, and the average saturation is 7.2%.