To provide a process for producing CeO.sub.2 fine particles having high
crystallinity, being excellent in uniformity of composition and particle
size and having a small particle size, and a polishing slurry containing
such fine particles.A process for producing CeO.sub.2 fine particles,
which comprises a step of obtaining a melt containing, as represented by
mol % based on oxides, from 5 to 50% of CeO.sub.2, from 10 to 50% of RO
(wherein R is at least one member selected from the group consisting of
Mg, Ca, Sr and Ba) and from 30 to 75% of B.sub.2O.sub.3, a step of
quenching the melt to obtain an amorphous material, a step of
precipitating CeO.sub.2 crystals from the amorphous material, and a step
of separating the CeO.sub.2 crystals from the obtained crystallized
product, in this order. A polishing slurry containing from 0.1 to 20 mass
% of such fine particles.