The present invention features a method for reducing the damage caused by free radicals, the method comprises administering a pharmaceutical composition that comprises at least a metal or its ions, at least a drug or an antioxidant that is carrier-protected/modified, and a drug carrier to a subject. Said carrier helps to preserve the anti-oxidative activity, and hence, prevents the decrease of the effect of the antioxidant against free radicals produced in the environment or body fluids and prolongs protection, and be used for reducing damage caused by radiation and adverse effects induced by chemotherapeutic drugs.