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Provided are : a new transition metal oxide catalyst which is comparable to noble metal catalysts; and an air electrode and an air secondary battery which include the catalyst. The catalyst is a catalyst for air electrodes which comprises a Brown millerite type transition metal oxide and is represented by the following general formula (1) : A2B1B2O5 (1) wherein A represents Ca, Sr, Ba, or a rare-earth element (RE); B1 is a metal atom which forms a tetrahedral structure in cooperation with oxygen atoms; and B2 is a metal atom which forms an octahedral structure in cooperation with oxygen atoms. The air electrode for metal/air secondary batteries includes the catalyst. The metal/air secondary battery has an air electrode including the catalyst, a negative electrode containing a negative active material, and an electrolyte interposed between the air electrode and the negative electrode.