In this paper,an equivalent circuit model of terahertz quantum casca de lasers (THz QCLs) is introduced by the revised three-level rate equations.This model account s for the influence of lattice temperature on steady characteristics of THz QCLs.Both the photon gain coefficient and the injection current efficiency depend on the lattice temperature in this model.The nonradiative scattering tim e,radiative spontaneous relaxation time and electron escape time are obtained by a self-consistent scheme.The mod el enables the analysis of the steady characteristics of THz QCL using general circuit analysis software,which overcomes the shortcomings of complex and long simulation time of numerical analysis method.Based on this new model,the steady characteristics of a 3.9THz device with lattice temperature in the range of 10－180K are investigated by using a circuit simulator (PSPICE).Results indicate that the model is practical and acc urate for THz QCL simulation study.