A cerium oxide nanoparticle is produced by adding an oxidant to a solution comprising a boron compound represented by formula (I) and a cerium (III) ion: wherein n represents an integer of 0 to 2, R represents any of an alkyl group having 1 to 4 carbon atoms, a phenyl group, and a tolyl group, and R′ represents any of a hydrogen atom, an alkyl group having 1 to 4 carbon atoms, a phenyl group, and a tolyl group, and when a plurality of Rs or of R's are present, the plurality of Rs or of R's are optionally the same or different.