Effect of O-2 adsorption on the magnetism of the rutile TiO2 (001) surface under different O-2 coverages were investigated. The surfaces that we considered for O-2 adsorption included the defect-free surface and the O-deficient surfaces with the charge states of 0, +1 and + 2. Nonmagnetic defect-free surface is difficult to absorb the O-2 molecule. Stabilities of oxygen vacancies with various valences at the top layer depend on their charge states, and the magnetic of the defective surface is related to V-o(+) instead of V-o(0) and V-o(2+). At low O-2 coverage, the endothermic adsorptions of O-2 molecule may introduce a nonzero local magnetic moment in the neutral reduced surface while its exothermic adsorption cannot. For the +1 or +2 O-deficient surface, the O-2 molecule is exothermically adsorbed on the surface and obtains some electrons to form a superoxide anion, which leads to the existence of magnetism. At high O-2 coverage, the chemisorptions of new O-2 molecule on the neutral O-2-preadsorbed substrate are related to the adsorption sites and O-O bond oriented. Endothermic adsorption of new O-2 molecule induces the magnetic moment on nonmagnetic O-2-preadsorbed substrate, while the substrate with the charge state of +1 or + 2 inhibits more O-2 molecule adsorptions.