Provided is a process for readily producing fine particles of a solid solution having a small particle size, comprising a solid solution of zirconia, ceria and a rare earth oxide in a desired composition, and being highly crystalline.The process for producing the fine particles of the solid solution comprises the following steps in the order named: obtaining a melt comprising, in terms of mol % on an oxide basis, from 5 to 50% ZrO2, CeO2 and RE2O3 (where RE is at least one member selected from rare earth elements other than Ce) in total, from 10 to 50% RO (where R is at least one member selected from the group consisting of Mg, Ca, Sr, Ba and Zn), and from 30 to 75% B2O3; quenching the melt to obtain an amorphous material; heating the amorphous material to obtain precipitates containing crystals of a solid solution with ZrO2, CeO2 and RE2O3; and separating the crystals of the solid solution from the precipitates to obtain fine particles of the solid solution.