CoPt alloy films of 40 nm thickness are prepared on MgO(111) substrates with and without Ru(0001) underlayer at 300 °C by radio-frequency magnetron sputtering. CoPt films with the close-packed plane parallel to the substrate surface grow epitaxially on the Ru underlayer as well as on the MgO substrate. Flat surfaces with the arithmetical mean roughness value of 0.2 nm are realized for both films. The crystal structure is determined by considering the atomic stacking sequence of close-packed plane and the order degree. The film formed on MgO substrate consists of an fcc-based L11 ordered crystal, whereas the film grown on Ru underlayer involves an hcp-based Bh ordered crystal in addition to the L11 ordered crystal. The order degrees of films formed on MgO substrate and Ru underlayer are 0.30 and 0.34, respectively. The L11 crystal consists of two variants whose stacking sequences of close-packed plane are ABCABC… and ACBACB…, while the Bh crystal is a single-crystal with the stacking sequence of ABAB… Formation of Bh crystal is promoted on the Ru underlayer. The film formed on Ru underlayer shows a strong perpendicular magnetic anisotropy reflecting the magnetocrystalline anisotropies of L11 and Bh crystals.