We studied the structural, electronic, and magnetic properties of a cubic perovskite BaFeO_3−δ (0 ≤ δ ≤ 0.5) within the density-functional theory using a generalized gradient approximation (GGA) and a GGA+U method. According to our calculations, BaFeO₃ in its stoichiometric cubic structure should be half-metallic and strongly ferromagnetic, with an extremely high Curie temperature (T_C) of 700-900 K. However, such an estimate of T_C disagrees with all available experiments, which report that T_C of the BaFeO₃ and undoped BaFeO_3−δ films varies between 111 and 235 K, or, alternatively, that no ferromagnetic order was detected there. Fitting the calculated x-ray magnetic circular dichroism spectra to the experimental features seen for BaFeO₃, we concluded that good agreement can be obtained when oxygen vacancies are included in our model. Thus, the relatively low T_C measured in BaFeO₃ can be explained by oxygen vacancies intrinsically present in the material. Since iron species near the O vacancy change their oxidation state from 4+ to 3+, the interaction between Fe⁴⁺ and Fe³⁺, which is antiferromagnetic, weakens the effective magnetic interaction in the system, which is predominantly ferromagnetic. With increasing δ in BaFeO_3−δ, its T_C decreases down to the critical value when the magnetic order becomes antiferromagnetic. Our calculations of the electronic structure of BaFeO_3−δ illustrate how the ferromagnetism originates and also how one can keep this cubic perovskite robustly ferromagnetic far above room temperature.