Based on the density matrix theory of quantum system, the spectra of optically pumped superradiant and cavity NH3 far-infrared (FIR) lasers were calculated by means of iteration method. The calculation showed that, compared with the optically pumped superradiant FIR laser, the cavity laser had a wider band spectrum of FIR emission and a higher output power under certain condition, moreover, the spectra of cavity laser had multi longitudinal-mode structure.