In the aim to stabilize novel three-dimensional perovskite oxides based upon SrCoO3−δ, we have designed and prepared SrCo1−xRexO3−δ phases (x = 0.05 and 0.10), successfully avoiding the competitive hexagonal 2H polytypes. Their performance as cathode materials in intermediate-temperature solid oxide fuel cells (IT-SOFC) has been investigated. The characterization of these oxides included X-ray (XRD) and in situ temperature-dependent neutron powder diffraction (NPD) experiments for x = 0.10. At room temperature, SrCo1−xRexO3−δ perovskites are defined in the P4/mmm space group, which corresponds to a subtle tetragonal perovskite superstructure with unit-cell parameters a = b ≈ ao, c = 2ao (ao = 3.861 and 3.868 Å, for x = 0.05 and 0.10, respectively). The crystal structure evolves above 380 °C to a simple cubic perovskite unit cell, as observed from in-situ NPD data. The electrical conductivity gave maximum values of 43.5 S·cm−1 and 51.6 S·cm−1 for x = 0.05 and x = 0.10, respectively, at 850 °C. The area specific resistance (ASR) polarization resistance determined in symmetrical cells is as low as 0.087 Ω·cm2 and 0.065 Ω·cm2 for x = 0.05 and x = 0.10, respectively, at 850 °C. In single test cells these materials generated a maximum power of around 0.6 W/cm2 at 850 °C with pure H2 as a fuel, in an electrolyte-supported configuration with La0.8Sr0.2Ga0.83Mg0.17O3−δ (LSGM) as the electrolyte. Therefore, we propose the SrCo1−xRexO3−δ (x = 0.10 and 0.05) perovskite oxides as promising candidates for cathodes in IT-SOFC.