The spin order in cubic perovskite SrFeO3 and BaFeO3 under high pressure is studied by density functional theory (DFT) calculation with local spin density approximation plus Hubbard U (LSDA+U ). At ambient pressure, A-type and G-type helical spin orders are almost degenerate in BaFeO3 whose lattice constant is 3.97Å. When the lattice constant is reduced to 3.85Å which is same as the lattice constant of SrFeO3 at ambient pressure, G-type helical spin order becomes stable, being consistent with SrFeO3. This is because superexchange interaction is enhanced as compared with double exchange interaction. Phase transition from helical spin state to ferromagnetic state in both SrFeO3 and BaFeO3 takes place if the lattice constant is further reduced to 3.70Å. This is because reduced local spin moment weakens the contribution from superexchange interaction. Our result agrees with recent experimental result of BaFeO3 under high pressure. Additionally, our calculation predicts that half-metal BaFeO3 at ambient pressure will become a good metal under high pressure.PACS numbers: PACS numbers: 75.30.Et, 75.50.Bb, 75.40.Mg Helical spin order in cubic perovskite AFeO 3 (A=Ca, Sr, Ba), where Fe 4+ is in a high spin configuration d 4 , has attracted lots of research interest for their potential application in spintronic devices. 1-3 All of them present helical spin order below 115 K, 134 K, and 111 K for A=Ca, Sr, and Ba, respectively. 4-7 The Fe3d electrons in these materials can be divided into two classes: conducting and localized electrons. Three localized electrons occupy t 2g orbitals and one electron occupies double degenerated e g orbitals. The interaction between conducting electron and localized electron is described by Hund coupling. In addition, charge-transfer energy ∆ defined as the energy cost to move an electron from oxygen 2p orbital to Fe3d orbitals shows a negative value, [8][9][10] implying that metallic conduction mainly occurs on oxygen band. The helical spin order can be understood from the competition of double exchange (DE) and superexchange (SE) interactions, the former and the latter of which favors ferromagnetism (FM) and anti-ferromagnetism (AFM), respectively. 11,12 It is well-known that electronic structure is tunable under high pressure. Phase transition from helical spin state to FM state in SrFeO 3 under the pressure of 7 GPa has been reported. 13 Very recently, the evolution of spin order in BaFeO 3 under pressure has been studied. 14 At ambient pressure, BaFeO 3 shows helical spin order, which changes to FM under very weak external magnetic field, ∼0.3 T. 7 The helical spin order is stabilized with increasing pressure, but FM finally becomes stable under pressure above 30 GPa. There is no structural phase transition, since the cubic symmetry of BaFeO 3 preserves up to 50 GPa. The electrical resistance decreases under high pressure.Hydrostatic pressure P reduces the lattice constant a in AFeO 3 . The compression of a leads to the increase of the hopping integral pdσ representing the hybridiza...