The relationship between electron quantum confinement and the energy dispersion of the surface plasmon in nanoscale thin Na layers adsorbed on Cu(111) at room temperature have been studied by high resolution electron energy loss spectroscopy. Screening effects due to electron quantum confinement occurring in this system cause the lowering of the surface plasmon frequency and, moreover, make the energy range of its dispersion curve larger than in thick alkali films. Landau damping of the plasma excitation was unexpectedly very efficient at small momenta. The dispersion curve of the Na surface plasmon was found to depend on the primary electron beam energy. Multipole surface plasmon at 4.70 eV was observed only for higher impinging energies.