The five-parameter Morse potential (5-MP for short) of interaction between adatom and metal cluster was constructed, and the adsorption of an O atom on Cu (100), Cu (110), Cu (111), Cu (211), and Cu (410) surfaces was studied by means of 5-MP. The data of the adsorption sites, adsorption geometry, binding energy, and eigenvibration, etc., for an O atom on the above surfaces are gained, and agree well with the experimental results. The diffusion of an O atom on plane surfaces is also dealt with. With regard to the adsorption of an O atom on the Cu (111) surface, calculation results suggest that the abnormally low experimental vibration of 29.4 meV of EELS (Dubois, L. H. Surf. Sci. 1982, 119, 399) arises from the effect of the sparse steps to the nearest neighbor 3-fold hollow site on the (111) terrace.