An FePt alloy thin film with L10 structure formed on a (001)-oriented polycrystalline underlayer or on a (001)-oriented single-crystal substrate may involve (100) variant with the c-axis lying in the film plane in addition to (001) variant with the c-axis normal to the substrate surface. In the present study, FePt(2-40 nm) films with and without MgO(2 nm) cap layers are prepared on MgO(001) single-crystal substrates by employing a two-step formation method consisting of low-temperature deposition followed by high-temperature annealing. Disordered FePt(001) single-crystal films with and without MgO(001) single-crystal cap layers epitaxially grow on the substrates at 200 °C. For the films thinner than 10 nm, the in-plane and out-of-plane lattices are respectively expanded and shrunk due to accommodation of the lattice misfit of film with respect to the substrate. With increasing the thickness up to 40 nm, the strain is relaxed. The phase transformation from A1 to L10 occurs when the films are annealed at 600 °C. The cap layer seems to prevent the strain release and to promote the phase transformation along the perpendicular direction. The c-axis orientation is controlled to be perpendicular by using the two-step method for the FePt films of thicknesses less than 10 nm with MgO cap layers. On the contrary, the film of 40 nm thickness with cap layer and the films of 2-40 nm thicknesses without cap layers involve small volumes of L10(100) variant. The order degrees of films with cap layers are higher than those of films without cap layers. The films with cap layers have flat surfaces with the arithmetical mean roughness values lower than 0.3 nm for all the investigated thicknesses, whereas an island-like surface is formed for the 2-nm-thick film without cap layer. The film consisting of only L10(001) variant shows a strong perpendicular magnetic anisotropy and a very low in-plane coercivity. Introduction of MgO cap layer is useful in aligning the c-axis perpendicular to the substrate surface, enhancing the L10 ordering, forming a flat surface, and achieving a strong perpendicular magnetic anisotropy.