Co/Pd multilayer films are prepared on fcc-Pd underlayers of (001), (011), and (111) orientations hetero-epitaxially grown on MgO single-crystal substrates at room temperature. The effects of underlayer orientation, Co and Pd layer thicknesses, and repetition number of Co/Pd bi-layer on the structure and the magnetic properties are investigated. fcc-Co/fcc-Pd multilayer films of (001), (011), and (111) orientations epitaxially grow on the Pd underlayers of (001), (011), and (111) orientations, respectively. Flatter and sharper Co/Pd interface is formed in the order of (011) < (111) < (001) orientation. Atomic mixing around the Co/Pd interface is enhanced by deposition of thinner Co and Pd layers, and Co-Pd alloy phase is formed. With increasing the repetition number (decreasing the thicknesses of Co and Pd layers), perpendicular magnetic anisotropy is promoted. Stronger perpendicular anisotropy is observed in the order of film orientation of (001) < (011) < (111). Perpendicular anisotropy of Co/Pd multilayer film is considered to be originated from the two sources; the interface anisotropy and the magnetocrystalline anisotropy associated with Co-Pd lattice shrinkage along the perpendicular direction. In order to enhance the perpendicular anisotropy of Co/Pd multilayer film, it is important to align the film orientation to be (111) and to enhance the lattice distortion along the perpendicular direction.