The effect of epitaxial strain on structural, magnetic and electronic properties of BaFeO3 perovskite oxide are investigated from first principles calculations, using the Density Functional Theory (DFT) plus the Hubbard approach (DFT+U) within the Generalized Gradient Approximation (GGA). Hybrid functional calculations, based on mixed exact Hartree-Fock (HF) and DFT exchange energy functionals, are also performed. For the ground state calculations,the DFT+U is found more suitable to describe the half metallic and ferromagnetic state of cubic BaFeO3. The possible occurence of oxygen octahedra rotations, Jahn-Teller distortions and charge orderings through biaxial strain are explored. The obtained results reveal that the Jahn-teller distortion is induced under tensile biaxial strain while the oxygen octahedra rotations and breathing are unusualy not observed. Then, the strained BaFeO3 is considered as a particular Jahn-Teller distorted perovskite with exceptional properties when compared to CaFeO3 and SrFeO3. These findings lead to a strain engineering of the JT distortions in BaFeO3, and thus for high fundamental and technological interests.