Spin-polarized electron energy loss spectroscopy is demonstrated to be an effective and unique tool to determine spin-wave dispersion curves of surfaces and ultrathin films over the whole Brillouin zone. The spin-wave dispersion curve of 8 monolayer Co on Cu(0 0 1) along the <1 1 0>-direction has the shape of a thin film spin dispersion curve with zero slope at the surface Brillouin zone. The cross-section of magnon excitation depends strongly on the energy E0 of the incident electrons and has a maximum around E₀=7 eV.