The influence of gravitational modulation on natural convection in a horizontal porous annulus is investigated in this paper. The mathematical model describing the phenomenon consists of the heat equation coupled by the hydrodynamics equations under the Boussinesq approximation. The derived system of equations with the stream function–temperature formulation is obtained and solved numerically using the alternating direction implicit method. It is shown that the convective stability of the fluid can be gained for small amplitudes of the vibration, while it will be lost for large ones. It was also observed that increasing the frequency has a destabilizing effect.