Natural gas hydrates have the properties of ice with a microporous structure and its concentration in sediments highly affects the wave velocity and attenuation. Previous studies have performed investigations based on the measurements of laboratory data, sonic-log data, and field data, whereas the variation trend of wave dissipation with increasing hydrate concentration at different frequencies is still unclear. We consider two different models to study this problem, both based on the Biot-Rayleigh double-porosity theory. In the first model, hydrate is part of the pore infill, unbonded from the grains, and brine saturates the remaining pore space. In the second model, hydrate forms a second skeleton and cements the grains. We obtain the P-wave velocity dispersion and attenuation as a function of the inclusion radius, porosity, and hydrate content. The analysis shows that the predictions of both models agree with the experimental data. At sonic log frequencies, the second model predicts much more attenuation, due to wave-induced local fluid flow (mesoscopic loss), and the behavior is such that below a given hydrate concentration the dissipation increases and then decreases beyond that concentration.