We focus on the electronic structures of small gas molecule (such as CO, H2O, NH3, NO, and NO2)-adsorbed stanene monolayers by first-principles method. The results show that H2O, NH3, and CO molecules are physisorbed on stanene monolayer, while NO and NO2 molecules are found to be chemisorbed on stanene with quite large charge transfer, sizable adsorption energy, and strong covalent (Sn-O) bonds. Moreover, our spin-orbit coupling calculations show that the band gaps of the molecule-adsorbed stanene monolayers can be tuned effectively. In particular, our results also show that when the biaxial strains and electric field are applied, the adsorption energies and charge transfer between gas molecules and stanene monolayers change dramatically, which indicates that external factors on stanene monolayers are highly preferred. These results indicate that stanene is promising for wide-ranging applications as superior gas sensors and electrical devices.