It has been found that the states at the level of the Fermi energy of undoped graphene sheet reduces to zero, making it difficult for the Cooper pairing of such a system to exist in its superconductive state. Instead, T-graphene, having physical properties close to graphene, exhibits a metallic behavior which means the existence of the available states for electrons near to Fermi level. For this two-dimensional metallic system, the gap equation of the s-wave superconductive state is derived based on the Bogoliubov de Gennes equation within the attractive Hubbard model. Using the gap equation, a nonzero critical temperature, Tc, is found for different amounts of electron–electron interaction, U. Tc has higher values when the system possesses electronic half band-filling, whereas the reverse is true when the system does not have half band-filling. However, close to band edges, Tc vanishes when U becomes small enough.