By using first-principles calculation, the interaction of O2 and H2O molecules with the pristine and the defective InSe monolayers is studied. It is predicted that the single Se and In vacancies exhibit significantly enhanced chemical activity toward the adsorbates compared with the perfect InSe lattice site, and the Se vacancies have a much higher chemical activity than the In vacancies. H2O molecule should be only physisorbed on the various InSe monolayers at ambient conditions, according to the calculated energies. The doping of the various InSe monolayers is discussed by the physisorbed H2O. The vacancies show a much higher chemical activity toward O2 than H2O. Although O2 molecules are still physisorbed on the pristine InSe monolayer, they will be chemisorbed on the defective InSe monolayers. Especially, our calculated energies suggest that the surface oxidation of the 2D InSe semiconductor should be dominated by the defects that expose under-coordinated host atoms, especially In atoms. Our theoretical results can help better understanding the doping and the oxidation of the 2D InSe semiconductor under ambient conditions.