Strain effects in epitaxial films can substantially enhance individual functional properties or induce properties which do not exist in corresponding bulk materials. The bcc α-Fe50Mn50 films are a ferromagnetic with a Curie temperature between 650 K and 750 K, which do not exist in nature can be manipulated through the tensile strain. In this study, γ-Fe50Mn50 epitaxial films grown on GaAs(001) using molecular beam epitaxy are found to structural transition from the face-centered-cubic (fcc, a = 0.327 nm) γ-phase to the body-centered-cubic (bcc, a = 0.889 nm) α-phase. For α-Fe50Mn50 epitaxial films, ferromagnetism is accompanied by structural phase transition due to the tensile strain induced by the differences of the thermal expansion between the film and the substrate. Moreover, by realizing in epitaxial films with fcc structure a tensile strain state, phase transitions were introduced Fe-Mn alloy system with bcc structure. These findings are of fundamental importance to understanding the mechanism of phase transition and properties of epitaxial CuAu-I type antiferromagnetic alloy thin films under strain.