Surface spin waves in a semi-infinite magnetic superlattice with a single-ion uniaxial anisotropy are investigated by use of the transfer-matrix method. The dispersion equations for surface spin waves are obtained. The authors find that not all of the structures of the superlattice can excite the surface spin waves and that the anisotropy term need not favour the excitation of surface spin waves, but that it will certainly influence the value of the energy of the excited surface spin waves.