Abstract: This paper presents a quantitative study of the critical current above which absolute instability would be excited in gyrotron traveling wave amplifier with the distributed loss waveguide. The dispersion property of a distributed-loss waveguide is derived in detail. The numerical results show that the threshold current depends on the skin depth of the waveguide wall, the magnetic field detuning and the perpendicular-to-parallel velocity ratio of the electrons. By designing the beam-wave interaction circuit with distributed-loss waveguide, the applied magnetic field and the velocity ratio, stable operation of the gyrotron traveling amplifier with wide band width and high efficiency can be ensured.