An air electrode catalyst for an air secondary battery includes a pyrochlore-type composite oxide having two or more crystal structures having a different amount of oxygen. A battery, according to some embodiments, includes an electrode group including an air electrode and a negative electrode stacked with a separator therebetween, and a container accommodating the electrode group along with an alkali electrolyte solution, wherein the air electrode includes the air electrode catalyst. The air electrode catalyst may have a pyrochlore-type composite oxide having a crystal structure represented by Bi2Ru2O6.92 and a crystal structure represented by Bi2Ru2O7.33.