The DFT approach is used for the first time to model the reaction of hydrogen with oxygen molecule adsorbed on the defective surface of In2O3(011). This reaction is crucial for hydrogen detection by In2O3 sensor. The activation energies are calculated using two mechanisms involving the formation of both an adsorbed water molecule and hydroxyl groups on the In2O3(011) surface. One hydroxyl group is formed due to the bonding of OH with the surface metal atom, and the other due to the bonding of hydrogen with oxygen of the lattice. Both reactions are characterized by the presence of a potential barrier and are exothermic. The activation energies of the two reactions are calculated by the climbing-image nudged elastic band method to be 0.99 eV and 0.98 eV. The results of the calculations are compared with available experimental data. It is also shown that the presence of a surface neutral oxygen vacancy leads to the formation of a vacancy state below the Fermi level, and the electron density is concentrated on the fourfold coordinated indium atom.