In order to solve the serious threat of SF 6 decomposed gases (H 2 S, SO 2 , SOF 2 , SO 2 F 2 ) to the stable operation of electrical equipment. In this study, the geometric structure, adsorption energy, density of states (DOS), sensitivity based on band structure and recovery time of H 2 S, SO 2 , SOF 2 , SO 2 F 2 on graphene and Rh -modified graphene (Rhgraphene) were investigated computationally by density functional theory (DFT). The geometric structure of Rhgraphene was optimized with an average Rh -C bond length of 1.891 & Aring;. According to the analysis of DOS and band structure, the electrical conductivity has a little effect of the Rh-graphene compared with pristine graphene, but Rh modification can regulate the band gap of graphene. The adsorption energy ( E ad ) and the sensitivity ( S ) at work temperature indicate that graphene has ideal adsorption and sensing properties for SO 2 and Rh-graphene reflects the excellent applicability as the SO 2 and SO 2 F 2 gases sensor with the sensitivity of approximately -99 % and -60 %, respectively. The Graphene/SO 2 system owns the minimum recovery time of 2154.3 ps. The recovery time of Rh-graphene/H 2 S and SOF 2 is several orders of magnitude smaller than Rh-graphene/SO 2 and SO 2 F 2 . The analysis of DOS and band structure was used to explain the sensing mechanism. The study would lay a theoretical foundation for the development of SF 6 decomposed gases sensor for electrical equipment insulation.