A composite material is constituted by fine nano-oxide particles, a dispersant, and a transparent resin material. The dispersant includes a polymer of vinyl monomer having a binding acidic group. When φ is a dimensionless number defined by an average particle size (nm) of the fine nano-oxide particles divided by nm, the polymer has a degree of polymerization of an integer of 3 or more and 8×φ or less with the proviso that the integer is a numerical value obtained by dropping a decimal fraction. The composite material is produced through a step of obtaining a dispersant comprising a polymer by polymerizing a vinyl monomer having a binding acidic group in the presence of polyamine or in an aqueous dilute dispersion, and a step of mixing the dispersant, fine nano-oxide particles, and a transparent resin material.