The invention relates to medicine, the chemical, pharmaceutical and food industries and may be used in the production of beverages and cosmetics with antioxidant activity (AOA). Hydrogen water is water saturated with molecular hydrogen. The water then displays AOA and decreases to negative values oxidation reduction potential (ORP). The aim of the present invention is to increase the AOA of hydrogen water without any undesirable irritating effects in humans. The aim is achieved by producing hydrogen water in the form of a water composition having molecular hydrogen dissolved therein under pressure and a small concentration of a food additive, an antioxidant. This composition provides a synergistic effect as evidenced by a manyfold increase in the AOA of the hydrogen water. The hydrogen water may be produced in the form of a bottled beverage and in the form of a moisturizing and cicatrizing antioxidant cosmetic in aerosol canisters where the gas propellant is hydrogen. The increased antioxidant activity of the hydrogen water imparts a higher quality and physiological value to same. The high reduction potential makes the hydrogen water "come alive".