A stable modified metal oxide sol which contains from 2 to 50 wt %, as calculated as metal oxides, of particles (c) comprising colloidal particles (a) of a metal oxide having primary particle diameters of from 2 to 60 nm, as nuclei, and a coating material (b) consisting of colloidal particles of an acidic oxide coated on the surface of the particles (a), and which has primary particle diameters of from 2 to 100 nm.