In this paper,an equivalent circuit model for terahertz quantum cascade lasers ( THz QCLs) is introduced by virtue of revised three-level multi-mode rate equations.This mod el accounts for influence of multi-mode on steady and optical spectra characteristics of THz QCLs.Both the p hoton gain coefficient and the spontaneous emission coupling coefficient depend on the wavelength in this model .The nonradiative scattering times,radiative spontaneous relaxation time and electron escape time are obtain ed by a self-consistent scheme. The model enables the analysis of the steady and optical spectra characteristics of THz QCL using general circuit analysis software,which overcomes the shortcomings of complexity and long simula tion time of numerical analysis method.Based on this new model,the steady and optical spectra charact eristics of a 2.47THz device with lattice temperature of 5K and 78K are investigated by using a circuit simula tor PSPICE.Results indicate that the model is practical and accurate for THz QCL simulation studies.