A synthetic catalyst providing superoxide dismutase activity consists essentially of monodispersed nanoparticles of cerium oxide having a crystal lattice containing cerium in mixed valence states of Ce.sup.3+ and Ce.sup.4+ wherein the Ce.sup.4+ valence state predominates and containing an enhanced Ce.sup.3+/Ce.sup.4+ ratio and an effective number of oxygen vacancies in the crystal lattice so as to increase catalytic efficiency. A method of making the synthetic catalyst includes dissolving hydrous Ce(NO.sub.3).sub.3 in water so as to form a solution, stirring the solution, adding hydrogen peroxide, heating and stopping when the solution develops a light yellow color.