The theoretical basis of superlattice terahertz Quantum Cascade Lasers(QCL) is to achieve the electron selective injection and the population inversion of the radiative states by energy level structure and wave function design. In this work, the power series method and the non-orthogonal basis diagonalization method were employed to calculate the electronic structures of the superlattice within the electric field, which are in excellent agreement with the experimental results in corresponding references. Then an active region design of resonant-phonon model was presented and the influences of the deviation of external field from the design value were discussed.