A novel transition metal oxide catalyst that is equivalent to precious metal catalysts, and an air electrode and an air secondary battery using this catalyst are provided. The catalyst is a catalyst for an air electrode including a brownmillerite-type transition metal oxide and represented by General Formula (1) below: A2B1B2O5  (1) where A represents Ca, Sr, Ba, or a rare earth element(RE), B1 is a metal atom that forms a tetrahedral structure together with oxygen atoms, and B2 is a metal atom that forms an octahedral structure together with oxygen atoms. Disclosed are an air electrode for a metal-air secondary battery that includes the catalyst, and a metal-air secondary battery that includes an air electrode including the catalyst, a negative electrode including a negative electrode active material, and an electrolyte intervening between the air electrode and the negative electrode.