The effect of hydrogen on the adsorption and dissociation of the oxygen molecule on a TiO2 anatase (001) surface is studied by first-principles calculations coupled with the nudged elastic band (NEB) method. Hydrogen adatoms on the surface can increase the absolute value of the adsorption energy of the oxygen molecule. A single H adatom on an anatase (001) surface can lower dramatically the dissociation barrier of the oxygen molecule. The adsorption energy of an O2 molecule is high enough to break the OO bond. The system energy is lowered after dissociation. If two H adatoms are together on the surface, an oxygen molecule can be also strongly adsorbed, and the adsorption energy is high enough to break the OO bond. However, the system energy increases after dissociation. Because dissociation of the oxygen molecule on a hydrogenated anatase (001) surface is more efficient, and the oxygen adatoms on the anatase surface can be used to oxidize other adsorbed toxic small gas molecules, hydrogenated anatase is a promising catalyst candidate.