In high-[Formula: see text] superconductors, electrons form pairs and electric transport becomes dissipation-less at low temperatures. The iron-based superconductors (FeSCs) have the highest superconducting (SC) transition temperature next to copper oxides. The gap structure and pairing mechanism for FeSCs are hotly discussed as a central issue since their discovery. A model Hamiltonian for the superconductivity in FeSCs is proposed by a tight-binding two-orbital model. The SC gap, conduction electron density of states, specific heat and energy band structure for the system are calculated. We have proposed here a [Formula: see text]-wave pairing symmetry of the form [Formula: see text] in the model in the mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently.