Considering the two-photon light shift (TPLS) effect and the Doppler shift effect, the model of the output frequency of the optically pumped THz gas laser has been built up. The influence of the TPLS and the Doppler shift effects on THz output frequency stability has been analyzed theoretically and numerically. Results indicate that, increasing the pump laser power may degrade the THz output frequency stability to some extent. When only considering the TPLS, with certain pump laser power, the THz frequency shift increases first and then decreases with the increasing of the pump laser frequency offset. In addition, the THz frequency shift tends to decrease gradually with the increasing of the gas pressure and the operating temperature. However, further considering the influence of the Doppler shift effect simultaneously, the THz frequency shift tends to increase nearly linearly with the pump frequency offset. The results provide reference to improve output frequency stability of the optically pumped THz gas laser.