Based on the dispersion equation of electromagnetic mode, the propagation characteristics in a lossy cylindrical waveguide are studied. The analytic formula of propagation constant for all modes in the waveguide is presented, which includes the effects of the thickness of the lossy layer. A large uumber of numerical calculations using the analytic formula and the dispersion equation have been carried out on the relations of the attenuation and phase constant with wave frequency, thickness and conductivity of the lossy layer. The analytic calculation results are in good agreement with those of the dispersion equation. This research is useful for selecting appropriate distributed wall losses for the stable and wide-band operation of gyrotron traveling wave amplifiers.