This paper, based on the rate equation theory, astablishes a model for optical pump waveguides to generate terahertz laser. By analyzing and solving the rate equation, the expressions of pump absorption coefficient, terahertz small-signal gain coefficient and terahertz output power are obtained. The calculation shows that the THz power increases first and reduces gradually with the increase of pressure of the working material, and it will increase with the increase of pumping power and the decrease of the output mirror reflectivity. The best working pressure increases with the rise of the pumping power. The number of particles in the excited state and the THz flux increase in the waveguide radial direction from the center, while the small-signal gain coefficient shows the opposite trend. Pump saturation, weak pump absorption and excited state terahertz absorption are the primary cause limiting the increase of the laser conversion efficiency. Results based on this model are in good agreement with the data from the relevant literature.