FeCo thin films were prepared on SrTiO₃(100), SrTiO₃(110), and SrTiO₃(111) single-crystal substrates by ultra-high vacuum molecular beam epitaxy. The film growth structure and magnetic properties were investigated. FeCo epitaxial thin films are obtained on these SrTiO₃ substrates at elevated temperatures with different crystal growth orientations. The nucleation and growth process of FeCo thin films on SrTiO₃ substrates vary depending on the orientation of the substrate and its temperature. FeCo(100) single-crystal thin films with an A2 structure are obtained on SrTiO₃(100) substrates at 500°C. FeCo epitaxial thin films with (110)_A2 and (211)_A2 planes parallel to the substrate surface are obtained on SrTiO₃(110) substrates. FeCo thin films epitaxially grown on SrTiO₃(111) substrates consist of two crystallographic phases having A2 and hexagonal structures with the (110)_A2 and (0001)_hex planes parallel to the substrate surface. The metastable FeCo(0001)_hex plane is presumably formed in order to relax the strain caused by the lattice mismatch at the FeCo/SrTiO₃(111) interface. The lattice constants of Fe₅₀Co₅₀ crystal with the hexagonal structure are estimated to be a = 0.251±0.004 nm and c = 0.457±0.005 nm. The magnetic properties of FeCo epitaxial thin films grown on SrTiO₃ substrates are influenced by the magnetocrystalline anisotropy and shape anisotropy caused by the roughness of FeCo islands that form the FeCo thin films.