Attention is observed experimentally in dry sedimentary rock samples at low frequency and high over burden stress. Currently well established attenuation mechanisms such as frictional sliding, squirt flow and viscous dissipation can not adequately explain the observed attenuation. WE propose a new mechanism for attenuation of seismic waves in sedimentary granular rocks. The origin of this mechanism lies in grain contact adhesion hysteresis. The propagation of seismic waves causes the gap width at grain contacts to vary. At high frequencies (10³ Hz), in liquid saturated rocks this leads to attenuation due to squirt flow. However, in dry rocks at low frequency (10^-2 Hz) this periodic oscillation in gap width (h) leads to energy dissipation due to hysteresis on a surface force vs. separation distance (h) diagram. The path taken when h is decreasing is different than when h is increasing (grains are being pulled apaprt). Surface forces and applied load play an important role in the magnitude of the calculated attenuation. The trends obtained from the proposed grain contact dhesion hysteresis mechanism are consistent with experimental observations. We show here that grain contact adhesion hysteresis causes energy dissipation without frictional sliding at grain contacts and give rise to frequency independent attenuation that increases with strain amplitude and decreases with overburden stress.  The conclusions obtained from the calculations are qualitative since they do not account for the complex distribution of asperity sizes and separations that would exist in a rock.  However, they provide a qualitative explanation for some hitherto unexplained experimental observations.