By using MgO∶LiNbO3 and undoped LiNbO3 crystals of 65 mm length, terahertz (THz) wave with the bandwidth of 0.34～2.90 THz is generated by using 1064 nm Q-switched Nd∶YAG laser with the energy of 12 mJ/pulse. Analysis shows that the polariton is an elementary excitation coupled from the electromagnetic TO phonon and incident photon. In the LiNbO3 crystal, the radiation frequency of polariton, which has the electromagnetic properties, can partly cover THz range, and the stimulated Roman scattering for the polariton can generate THz wave. Furthermore, the radiation theory of polariton shows the dispersion characteristic of the polariton can determine the possibility of the crystal generating the THz wave, as well as its bandwidth range.