We present a theoretical model study of superconductivity for iron-based high-[Formula: see text] superconductors in s[Formula: see text]-wave symmetry, considering two degenerate orbitals and the electron hopping up to the third nearest neighbor as a two-orbital model. The analytic expression for the temperature dependence of the superconducting order parameter is derived by Zubarev’s technique of double time single particle Green’s function method and solved self-consistently. The effect of inter orbital hopping on the superconducting energy gap parameter and electronic specific heat is studied.