A nanocrystal cerium zirconium composite oxide and its preparation and application are disclosed. The nanocrystal cerium zirconium composite oxide of the present invention comprises 4-98% by weight of CeO.sub.2 and 1-95% by weight of ZrO.sub.2, the crystalline particle size thereof is 100 nm or less, and the ignition loss thereof after igniting at 900.degree. C. for one hour is smaller than 5%.