We have grown epitaxial Co films on a single monolayer of Pd on Cu(100) substrate at room temperature. The interlayer of Pd was grown by pulsed laser deposition, whereas the Co layer was prepared by thermal deposition. A layer-by-layer growth mode continues until at least 11 ML Co layers in comparison to 4 ML on Pd(100)substrate, which is due to a reduced lattice mismatch between Co and the Pd/Cu(100) substrate in comparison to the Co on Pd(100) system. Compared to Co films on Pd(100), a larger slope of the thickness dependence of longitudinal magneto-o ptical Kerr rotation has been found in the Co/Pd/Cu(100) films with thickness ab ove 2 ML. We have also found an increase of longitudinal magneto-optical Kerr ro tation for Co/Pd/Cu(100) in comparison to Co/Cu(100) system which may be attribu ted to the Co/Pd interface effect.