The reflection of elastic waves at the surface of a couple-stress elastic half-space with a viscoelastic support is studied in this paper. Different from the classical elastic solid, there are: a non-dispersive dilatational propagating wave, a dispersive transverse propagating wave and a dispersive evanescent wave in a couple-stress elastic solid. The boundary conditions at the visco-elastically supported surface of a couple-stress elastic half-space include the couple-stress vector and the rotation vector, which disappear in the classical elastic solid. They are used to obtain a set of linear algebraic equation, from which the amplitude ratios of reflection waves with respect to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. At last, the influence of the boundary parameters that reflect the mechanical behavior of a viscoelastic support on the amplitude ratio, the phase shift and the energy partition of reflection waves are discussed based on the numerical results. Both the incident longitudinal displacement wave (the P-wave) and incident transverse displacement wave (the SV-wave) are considered. It is found that the instantaneous elasticity and the delayed viscosity of a viscoelastic support have different influences on the reflection waves.