For reducing mode density and lowering the risk of spurious mode competition in THz gyrotron, the mode-selective confocal waveguide system is adopted for high frequency circuit of 140 GHz HE06 mode confocal waveguide Gyrotron Traveling Wave Tube(Gyro-TWT) amplifier. Based on the analysis of RF system, the theoretical analysis about electron beam and waves interaction is presented. The structure and operating parameters of the gyro-TWT are determined by analysis of field distribution, diffraction loss, coupling coefficient and interaction between electron beam and wave. Nonlinear theory is utilized to calculate the amplifier, and nonlinear analysis shows that the interaction circuit can generate a saturated peak power of 12 kW, corresponding to a saturated gain of 38 dB, an efficiency of 17.1%, and a 3 dB bandwidth of 6 GHz at 140 GHz when utilizing a 35 kV, 2 A electron beam with 0.75 of the ratio of the transverse velocity to the longitudinal velocity.