Based on first-principles calculations, we have studied the stability and the structural and electronic properties of the indium selenide (InSe) monolayers with the adsorbed small molecules, including CO, H2O, NH3, N-2, NO2, NO, and O-2. It is found that all the molecules are physisorbed on the InSe monolayer surface and act as electron acceptors for the InSe, except NH3 which is found to be an electron donor. Furthermore, for most of the molecules studied, the adsorption cannot induce obvious changes in the band structures near the Fermi level compared with those of the pristine InSe monolayer. However, it is noted that the adsorbed InSe monolayers have new in-gap states induced by the open-shell molecules (NO2, NO, and O-2), which may trigger some new effects on the optical properties of the materials. Our theoretical findings suggest that two-dimensional InSe nanomaterials hold great promise for fabricating gas sensors based on a physisorption-based charge transfer mechanism. (C) 2017 Elsevier B.V. All rights reserved.