It is an important way by detecting SF6 decomposition products to evaluate the insulation condition of SF6 insulated power equipment. In this paper, N3&Ni doped 555-777graphene (N3&Ni-graphene) is proposed as a new gas sensor to detect the characteristic components of SF6 decomposition products: H2S, SO2, SOF2 and SO2F2. In order to get insights into the gas sensing mechanism, the geometry structures, electron structures and conductivity are analyzed by simulation method based on density functional theory. The calculation results show that N3&Ni dopant can improve the conductivity and surface activity of 555-777graphene. Specifically, H2S and SO2 absorbing on N3&Ni-graphene surface will increase the conductivity obviously, while the other two kinds of gas molecules will decrease the conductivity. The sensitivity of H2S is greater than SO2 according to the changed value of energy gap. It is also indicated that N3&Ni-graphene can absorb the above four characteristic components stably with high adsorption energies, complex orbital hybridizations and multi-level charge transfer. This work will provide some theoretical guidance to develop a novel gas sensor to evaluate the insulation condition of SF6 insulated equipment.