SF6 decomposition products: SO2, SOF2, and SO2F2 were investigated using Al24N24 nanocage based on density functional theory (DFT). The adsorption properties were studied by analyzing adsorption energy, charge transfer, frontier molecular orbitals, and density of states (DOS). Our calculation suggests that the adsorption ability of Al24N24 to SO2 and SOF2 are stronger than adsorption of SO2F2 gas due to chemical adsorption. The results show that Al24N24 nanocage plays crucial role for detecting SF6 decomposition gas with high sensitivity and selectivity.