Particles for catalyst which have a function of absorbing and desorbing oxygen, the particles comprising an iron compound in which an element, other than Fe, having two valences is solid-soluted in an oxide of Fe having three valences, and a method for producing the particles for catalyst which comprises precipitating a precipitate containing Fe having three valences and an element, other than Fe, having two valences from a solution containing ions of Fe having three valences and ions of the element, other than Fe, having two valences, and drying and firing the precipitate to produce the particles.