A metal oxide dispersion contains a metal oxide and a phosphorus compound. It has an increased refractive index and higher transparency while eliminating a reduction in abrasion resistance. The problem of producing a metal oxide dispersion and a polymerizable composition, each of which serves as the starting material for the polymer; and the problem of producing the organic-inorganic hybrid polymer or the occurrence of cracks can be prevented during the production procedure. This further relates to the problem of producing an anti-reflective film which uses the organic-inorganic hybrid polymer and exhibits high performance. These dispersions are the suspensions of very small particles in any organic solvent or water. The particles can settle down in dispersion but it should be shaken or mixed by ultra-sonication before use. Metal and oxide dispersions have many uses in industries like automotive paints, industrial coatings, architectural coatings, cosmetics, and wood finishes.