Optically pumped FIR lasers give only discrete spectrums. This property restricts the practical use of lasers. Since 1977, many research works have been done to tune the output frequency of FIR laser, of which some are tried to find the possibility of tuning the laser lines by changing the pumping frequency continuously. But it is not easy to get an accurate result due to the complexity of theoretical calculation especially for quantum system of more than three energy levels. In this research work, two photon processes in four levels system have been studied by means of graph theory, which was developed by T. A. DeTemple et al. It was found that the output frequency of optically pumped FIR laser could be tuned with a frequency range equal to the frequency difference of two FIR transition frequencies. The tuning curves of FIR frequency and the curves of system gain coefficient vs. pump detuning frequencies were given.