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In gas-insulated switchgear (GIS), partial discharge (PD) can be monitored by detecting sulfur hexafluoride-nitrogen (SF₆-N₂) decomposition components. In this paper, silver oxide (Ag₂O) modification was introduced to improve the gas-sensing properties of graphene-like indium nitride (InN). The adsorption process of NO₂, SO₂F₂, SOF₂ and SOF₄ on Ag₂O-InN was simulated based on the first principles calculation and density functional theory (DFT). The gas sensing mechanism was revealed by density of states theory and molecular orbital theory. It is found that Ag₂O doping greatly improves the adsorption properties of InN to NO₂ and SOF₂ molecules. The adsorption capacity of Ag₂O-InN to the four gas molecules is: NO₂ > SOF₂ > SOF₄ > SO₂F₂. All adsorptions can proceed spontaneously, and the gas molecules are electron donors and Ag₂O-InN is an electron acceptor. Through the analysis of recovery time, it is found that NO₂ is difficult to desorb from the substrate due to the significant adsorption energy of −2.201 eV, while SOF₄, SOF₂ and SO₂F₂ have a moderate adsorption energy of −0.185 eV, −0.754 eV and 0.173 eV and extremely short desorption time. The conductivity of the whole system changed after these four gases were adsorbed on the Ag₂O-InN monolayer. In summary, Ag₂O-InN can be used as NO₂ adsorbent and gas sensors to detect SOF₄, SOF₂ and SO₂F₂. This paper provides a method for on-line monitoring of partial discharge in GIS.