We propose a new mechanism for attenuation of seismic waves in rocks. It is shown that grain contact adhesion hysteresis leads to energy dissipation without having to invoke frictional sliding at grain contacts. Adhesion hysteresis gives rise to frequency independent attenuation that increases with strain amplitude for large strains and decreases with overburden stress. We can obtain qualitatively correct trends that show the effect of fluid saturation, pore structure and grain size through simple models for granular sedimentary rocks.