Terahertz (THz) spectroscopy is expected as a new technique for nondestructive inspection of pharmaceutical tablets, because THz waves pass through a wide variety of pharmaceutical materials. We have been developing a frequency-domain THz spectrometer with an injection-seeded THz parametric generation (is-TPG) technique. In this study, the frequency range of the spectrometer was successfully expanded to 0.9-4.2 THz by generating widely tunable THz waves by shifting a nonlinear crystal to balance gain and absorption of the THz waves in the crystal, and detecting the THz waves with an angle-compensation method that utilized the dispersion of the crystal. Absorption spectra of the crystal polymorphs of carbamazepine forms I and III were obtained with the THz spectrometer, and these polymorphs were identified by specific absorption peaks related to their solid state.