The aim of the present paper is to study the wave propagation in anisotropic thermoviscoelastic medium in the context Green-Naghdi theories of type-II and type-III. It is found that there exist two quasi-longitudinal waves (qP, qT) and two transverse waves (qS1, qS2). The governing equations for homogeneous transversely isotropic thermoviscoelastic are reduced as a special case from the considered model. Different characteristics of waves like phase velocity, attenuation coefficient are computed from the obtained results. Viscous effect is shown graphically on different resulting quantities for Green-Naghdi theories of type-II and type-III. From the present investigation, some particular cases of interest are also deduced.