Abstract: The nuclear ground state properties of the superheavy nucleus ²⁹⁶Og, such as the potential energy surface, single-particle energy spectrum, two-neutron separation energy and α-decay energy, are studied with the volume, surface and mixed pairings based on the SLy4 interaction in the framework of the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) theory. It is found that 1) The ground state shape of ²⁹⁶Og is nearly spherical with the volume and mixed pairings. However, the shape coexistence of ²⁹⁶Og is predicted with the surface pairing. 2) The super-deformed states are predicted by all of the three kinds of pairings. The binding energy, potential well depth and excitation energy of the super-deformed states are influenced by the pairings. At the same time, the surface pairing effect on the properties of the super-deformed states is the most evident. 3) The pairings have certain influence on the shell structure, two-neutron separation energy, α-decay energy and α-decay half-life of ²⁹⁶Og and the impact from the surface pairing is the strongest. Moreover, the order of magnitude of α-decay half-life is varied occasionally owing to the change of the α-decay energy caused by the pairings.