In this paper the surface Josephson plasma wave (SJPW) excitation on the periodically-modulated layered superconductor is considered. It is shown that the absorption of the incident electromagnetic wave can be substantially increased at certain incident angles due to the resonance excitation of the surface waves. The optimal combinations of the parameters of the problem (modulation amplitude, wavelength, incident angle) corresponding to maximum SJPW excitation and the effect of the total suppression of specular reflection (TSSR) are found for a real medium (Bi2212).