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We present an efficient parameterized tight-binding (TB) model which can induce the energy bands that are consistent with results from ab-initio calculations. Besides the comparison of our simple TB model to previous ones, we also supplement further neighbor interactions into the TB Hamiltonian to analyze the band structure and consider the impact of each type of TB parameters such as onsite and hopping energies, overlap terms of wave functions on the shape and position of the energy bands. Then a set of appropriate parameters is selected to reproduce reasonably important characteristics of the band structure captured by ab-initio calculations, particularly at the low energy region near the Fermi level, which is relevant for many applications. Moreover, the TB model is applied to predict the impact of a vertical electric field on the electronic properties and the thermoelectric Seebeck effect of penta-graphene. It unveils that the bandgap is strongly modulated under the external field and the intrinsic Seebeck coefficient of penta-graphene is found to be 67 times as high as that of graphene.