The flexoelectric effect describes the coupling of polarization to strain gradient, which has increasingly attracted interest in perovskite oxide materials. The perovskite oxide superlattice containing epitaxial relaxation or intrinsic surface tension or curvature, together with its high dielectric constant, is a highly desirable candidate for high flexoelectricity. In this work, the flexoelectric coefficients of ¹SrTiO₃/¹BaTiO₃ superlattice, which is composed of alternating single atomic layers of SrTiO₃ and BaTiO₃, are systematically investigated with first principle density functional theory calculations. Various supercell sizes are used to minimize the discrepancy between the gradient values of the fixed atoms and relaxed atoms. It is found that the strain gradients of the constrained A-site atoms and the relaxed B-site atoms are almost the same when the supercell sizes are 1×1×24 for longitudinal flexoelectric coefficient, 7×1×16 for transverse flexoelectric coefficient and 3×1×28 for shear flexoelectric coefficient. Calculation results demonstrate that the transverse flexoelectric coefficient and shear flexoelectric coefficient of ¹SrTiO₃/¹BaTiO₃ superlattice are about one order of magnitude larger than its longitudinal flexoelectric coefficient. Even though its longitudinal flexoelectric coefficient decreases slightly compared with its constituent compounds, both transverse coefficient and shear flexoelectric coefficient are about several times higher than the counterparts of its constituent compounds, respectively. Hence, the overall flexoelectric coefficient of ¹SrTiO₃/¹BaTiO₃ superlattice is enhanced several times in magnitude. There exist a large number of interfaces inside the perovskite oxide superlattice with alternating single atomic layers of SrTiO₃ and BaTiO₃, which potentially stimulate the redistribution of charge carriers, orbitals and spins of the atoms at the interface and promote the interfacial strain gradient. The stacking order of the superlattice atoms has a profound influence on the flexoelectric properties. These studies present an alternative approach to fabricating better flexoelectric materials for the applications of electromechanical equipment.