The excitation of multiple surface-plasmon-polariton waves, all of the same frequency but different polarization states, phase speeds, spatial profiles and degrees of localization, by a compound surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied using the rigorous coupled-wave approach. Each period of the compound surface-relief grating was chosen to have an integral number of periods of two different simple surface-relief gratings. The excitation of different SPP waves was inferred from the absorptance peaks that were independent of the thickness of the rugate filter. The excitation of each SPP wave could be attributed to either a simple surface-relief grating present in the compound surface-relief grating or to the compound surface-relief grating itself. However, the excitation of SPP waves was found to be less efficient with the compound surface-relief grating than with a simple surface-relief grating.