Sr0.95Ce0.05CoO3−δ (SCCO) particles loaded with copper nanoparticles on their surface are shown to be excellent, low-cost, and stable bifunctional catalysts for the oxygen-reduction and oxygen-evolution reactions (ORR and OER) in aqueous solution. Evidence for the presence of Ce3+ and Co2+ as well as Co4+ and Co3+ ions revealed by XPS measurements as well as XRD analysis indicates that a CeCoO2.5 brownmillerite phase may be extruded to the surface. A surface Co4+/Co3+ couple is known to be a good OER catalyst. The performance of the SCCO-based catalysts is better at higher current rates (>0.1 mA cm−2) than that of Vulcan XC-72 and even close to that of the 50% Pt/carbon-black catalyst. This catalyst could be used in a metal/air battery or a PEM fuel cell as an efficient and stable bifunctional catalyst.