Based on the predecessor′s theoretical achievements, probabilistic analysis for realizing terahertz (THz) radiation of lasers by strict calculation method is given. The distributions of conduction subband structure and the electron wave function of GaN-based three-level quantum cascade lasers are solved with the transfer matrix method by Matlab, the polarization field of material is analyzed detailedly. The relationships among dipole matrix element, applied external electric field, the barrier layer of Al composition and energy difference of conduction subband in near-resonant conditions are calculated, and their effects on properties of lasers are studied. The analysis of the results shows that realizing stimulated radiation is very strict, it is proper that the composition of Al is 0.15 or 0.16, and the external electric field intensity is greater than 63 kV/cm，but is not too large. In this case, the near-resonant conditions can be satisfied, so that population inversion is realized to reach THz quantum cascade lasing. While the largest dipole matrix element is obtained at the composition of Al of 0.15 and the external electric field intensity of 69.0 kV/cm, indicating that transition probability is also the largest. It is beneficial for the properties of lasers, thus the preferable active region can be constructed for quantum cascade lasers.