Abstract We study the propagation and dissipation of Alfvén gravity waves in the solar corona, considering viscosity as a damping mechanism, and derive a general dispersion relation for Alfvén gravity waves under WKB and Boussinesq approximation. We find that in the presence of viscosity, the wave normal surfaces do not differ significantly from the results obtained in an ideal MHD. From dissipation point of view, we find that for the wave frequency less than the Brunt–Väisälä frequency (i.e., ω ¯ < 1 ) there are two types of damping, one is strong damping when L D ∼ λ and the other is weak damping when L D ≫ λ. For the wave frequencies greater than the Brunt–Väisälä frequency (i.e., ω ¯ > 1 ), however, we get only weak damped oscillations. Thus, Brunt–Väisälä frequency separates regimes of wave frequency in which damping is weak or strong.