Co epitaxial thin films were prepared on MgO substrates of (100), (110), and (111) planes by molecular beam epitaxy. The nucleation of Co crystal on MgO substrate varies depending on the substrate orientation and the substrate temperature. On MgO(100) substrates, Co(112^^-0) epitaxial bi-crystalline films with hcp structure are obtained at temperatures higher than 300℃, whereas a Co epitaxial film prepared at 100℃ includes fcc(100) crystal in addition to hcp(112^^-0) crystal. Co(110)_<fcc> single-crystal films with fcc structure are formed on MgO(110) substrates. Co films consisting of fcc(111) and hcp(0001) crystals epitaxially grow on MgO(111) substrates. With increasing the substrate temperature, the volume ratio of hcp(0001) crystal increases, whereas that of fcc(111) crystal decreases. High-resolution transmission electron microscopy shows that atomically sharp boundaries are formed between the Co films and the MgO substrates, where misfit dislocations are preferentially introduced in the films at the interfaces. The presence of such dislocations relieves the strain caused by the lattice mismatches between the films and the substrates.