Abstract: A catalyst for purifying exhaust gases includes a porous support; a cerium oxide or a solid solution of a cerium oxide and a zirconium oxide in a state of mutual solid solution, loaded on the porous support; and a noble metal element loaded on the porous support. The cerium oxide or the solid solution has an average particle diameter of from 5 to 100 nm. The cerium oxide is present in the solid solution in an amount of from 0.2 to 4.0 by molar ratio with respect to the zirconium oxide therein. The catalyst can be prepared by: coating and calcinating on a support substrate a slurry of a cerium oxide sol, a cerium oxide sol and a zirconium oxide sol, on a solid solution powder of a cerium oxide and a zirconium oxide in a state of mutual solid solution; and loading a noble metal element thereon.