We have studied, for the first time, the energy and the linewidth dispersio
n of a plasmon in a dense two-dimensional electron system in a metallic sur
face-state band on a silicon surface. As expected from the considerably hig
h effective density and long Fermi wavelength of the system, the plasmon en
ergy dispersion exhibited,an excellent agreement with the nearly,free-elect
ron theory. However, in a small wave number region below the Landau edge,we
have observed an anomalous linewidth dispersion which nearly free-electron
theories do not predict.