First-principle calculations were carried out to simulate the three decomposition gases (SO2, SOF2, and SO2F2) of sulfur hexafluoride (SF6) on Ga-doped MoS2 (Ga-MoS2) monolayer. Based on density functional theory (DFT), pure MoS2 and multiple gas molecules (SF6, SO2, SOF2, and SO2F2) were built and optimized to the most stable structure. Four types of Ga-doped positions were considered and it was found that Ga dopant preferred to be adsorbed by the top of Mo atom (TMo). For the best adsorption effect, two ways of SO2, SOF2, and SO2F2 to approach the doping model were compared and the most favorable mode was selected. The adsorption parameters of Ga-MoS2 and intrinsic MoS2 were calculated to analyze adsorption properties of Ga-MoS2 towards three gases. These analyses suggested that Ga-MoS2 could be a good gas-sensing material for SO2 and SO2F2, while it was not suitable for SOF2 sensing due to its weak adsorption. This work provides a theoretical basis for the development of Ga-MoS2 materials with the hope that it can be used as a good gas-sensing material for electrical equipment.