The density functional theory (DFT) is used to investigate the gas sensing properties of both pristine and n-type InSe monolayers to SF6 decomposition products. The adsorption energy, electron transfer, the band structure and the density of states (DOS) of both types of InSe monolayers are analyzed. In addition, the response and recovery properties, and the selectivity of these InSe monolayers to five types of gas molecules (SO2, SOF2, SO2F2, H2S and HF) are investigated. In the study, the n-type InSe monolayers are doped with F and I atom, respectively. The results show that the interactions between the pristine InSe monolayer and the gas molecules are relatively weak. After only being doped with F atom, the chemical interaction between InSe and SO2 is dramatically enhanced, with significantly increased adsorption energy and enhanced electron transfer. The adsorption of SO2 also leads to conspicuous changes of electronic properties of the F and I doped InSe monolayers, making the strong n-type properties disappear. The high selectivity and acceptable recovery properties of InSe-F monolayer to SO2 indicate that it is promising to use the InSe-F monolayer for detecting SF6 decomposition products. This study provides a theoretical basis for future application of InSe monolayers or ultra-thin InSe based gas sensing devices.