FePd-alloy thin films of 40 nm thickness are prepared on MgO single-crystal substrates of (001), (110), and (111) orientations by employing a two-step method consisting of deposition at a low temperature of 200 °C followed by annealing at a higher temperature in a range from 300 to 600 °C. The influences of substrate orientation and annealing temperature on the ordered phase formation and the surface roughness are investigated. FePd films with disordered A1 structure grow epitaxially on MgO substrates of all the orientations at 200 °C. Transformation from A1 to L10 phase starts to be observed in FePd films formed on the respective MgO substrates after annealing at 300, 500, and 600 °C. With increasing the annealing temperature up to 600 °C, the order degrees of FePd films formed on MgO substrates of (001), (110), and (111) orientations respectively increase to 0.63, 0.29, and 0.33. The films before annealing have very flat surfaces and the flat surfaces are kept after annealing for all the substrate orientations and the investigated annealing temperatures. The arithmetical mean surface roughness values of FePd films formed on MgO(001), (110), and (111) substrates after annealing at 600 °C are 0.2, 0.2, and 0.3 nm, respectively. The L10-FePd film formed on MgO(001) substrate shows a perpendicular magnetic anisotropy, whereas the L10-FePd films formed on MgO(110) and (111) substrates have in-plane anisotropies. The magnetic anisotropy is influenced by the c-axis distribution and the order degree.