The influence of interfaces on the magneto-optical Kerr effect in the Co/Ni multilayer has been investigated. It was found that the magnetic-optical Kerr rotation varies with the numbers of interfaces (x) in the Co/Ni multilayer,which indicated that the interface states play an important role in the Kerr effect. Moreover, ellipticity and optical constants n and k are also found to vary with x. Some possible mechanisms have been discussed.