Robust ferromagnetism with high Curie temperatures (TC), especially above room temperature, in perovskite oxides is extremely rare because the oxygen-mediated antiferromagnetic superexchange generally dominates in these nearly cubic perovskite lattices. Fe4+ ions show potential to promote magnetism responses due to more apparent hybridization between Fe4+ and oxygen orbitals with Jahn-Teller distortion, while this distortion also sacrifices the stability of Fe4+-based oxides. Here, by engineering oxygen vacancies, we report robust ferromagnetism with TC above 600 K in cubic perovskite BaFeO3-δ films epitaxially grown on KTaO3 substrates. A mixture of Fe4+ and Fe3+ cations, mediated by the oxygen vacancies, was identified to be responsible for the robust magnetism as revealed by atomic-scale studies and element-selective circularly polarized X-ray absorption spectra. This study indicates that spin-state ordering could be manipulated in a simple perovskite oxide by engineering oxygen stoichiometry and would be of significance toward future technological applications.