Elastic wave propagation has been explored in an infinite granular thermoelastic medium rotating with constant speed. The elastic and thermal parameters of the granular medium are taken to be randomly fluctuated so that the medium represents the randomly fluctuating inhomogeneous medium. The method of smooth perturbation has been used, which requires the inversion of a deterministic differential operator to find the solution of governing equations in the relevant media. The analysis is based on the dynamics of granular medium as propounded by N. Oshima. All field parameters are functions of space vector and time. A general dispersion equation for waves propagating in the rotating random granular generalized thermal elastic medium has been obtained. The compression and shear wave propagations have been studied. It has been pointed out that in the case of compression waves, the mean and auto-correlation function of the thermo-mechanical coupling parameter greatly influence the mean wave propagation. For shear waves, however, randomness has no effect on wave propagation. Effects of non-random granular elastic medium, randomness and rotation of the frame of reference are discernible from analyses of dispersion equations. The study may find applications in soil mechanics, seismology and oil-prospecting. Computational results have been shown. (C) 2015 Elsevier Ltd. All rights reserved.