We have studied ultra-thin Co/Au(111) films with perpendicular magnetic anisotropy by means of spin-wave Brillouin scattering. The ultra-thin Co films with thicknesses from 1 to 7 monolayer (ML) were grown by molecular beam epitaxy on 1 ML Au underlayers without intentional substrate heating. With 2 or more MLs of Co, spin-wave excitations are clearly observed. We find the magnetic field dependence of the spin-wave energy can be quantitatively explained by a calculation including out-of-plane magnetization due to uniaxial perpendicular magnetic anisotropy. The first-order perpendicular anisotropy constant systematically increases as the Co thickness decreases from 7 to 3 ML. The second-order perpendicular anisotropy constant is much smaller than that expected in Co(0001) bulk and also increases as the Co thickness decreases. The physical origin of the thickness dependence of the perpendicular anisotropy is discussed. We find the field dependence of the scattering intensity is different between Stokes and anti-Stokes processes. Finally, with 2 ML of Co, significant broadening of the spin-wave spectrum is observed, as well as the degradation of the perpendicular anisotropy. We believe this is the result of the effect of magnetic inhomogeneities due to the structural imperfections. ©1997 American Institute of Physics.