A Ka-band second-harmonic gyrotron traveling wave amplifier with multi-stage loss waveguide was studied. By stability analysis, the parameters were determined. A 35GHz TE02 mode second harmonic three-stage distributed-loss gyro- TWT was presented and the optimized design was carried out. Then the nonlinear analysis was presented to study the interaction between electron beam and wave. The results indicate that the interaction structure can suppress the parasitic modes effectively, meanwhile, 125kW output power and 39dB gain are obtained when the beam velocity spread is 3%. The 3dB bandwidth is 4.3%.