The relationship between the interfacial roughness and the giant magnetoresistance (GMR) in Co/Cu superlattices has been studied. The results have been understood with an s - d scattering model on the assumption that d states are bound in magnetic layers. The GMR in Co/Cu superlattices mainly comes from the spin-dependent s - d scattering in the Co layers, and the interfacial scattering is less spin-dependent than bulk scattering. This is because of the attenuation of the wave function of d states at interfaces.