The excitation of surface plasmons (SPs) with a strip grating at the boundary of an unmagnetized overdense plasma has been investigated theoretically and experimentally. An incident electromagnetic radiation was p-polarized at the frequency of 5 GHz. Experiments showed that when the plasma density was four times higher than the critical density with the grating present, and the SPs could be excited at the boundary of the overdense plasma. Contribution of the glass layer in the formation of the SP dispersion relation was examined. When the incident electromagnetic radiation was coupled into SPs the coupling order with the effective permittivity was simulated qualitatively. We find that the existence of SPs at the boundary of overdense plasma indicates that the reflection coefficient of the incident electromagnetic radiation reaches its minimum and even becomes total absorption. In this work the plasma density was diagnosed by a Langmuir double probe.