The effects of strain and interface roughness at the Co/Pd interface are investigated from the viewpoint of perpendicular magnetic anisotropy (PMA) using the DV-Xα cluster model calculation method. It is found that spin projected occupation number ratio of magnetic quantum number |m| = 2 for the Co 3d electrons enhances by expanding the lattice within a close-packed plane of fcc stacking and, hence, enhances the PMA. Rough interface decreases the spin projected occupation number ratio of |m| = 2 and, hence, decreases the PMA. These results explain the PMA properties of Co/Pd multilayers fabricated using molecular beam epitaxy (MBE) technique and RF sputtering techniques.