A pulse prototype of a W-band TE01 mode gyrotron traveling-wave tube (gyro-TWT) amplifier is designed, and it features high gain and broadband capabilities. The TE01 mode input coupler is constructed by mounting a sapphire pill-box window onto a Y-type mode converter. The high power output window will employ a triple-sapphire-disc configuration to achieve return loss lower than -30 dB over a bandwidth of 8 GHz. To suppress the spurious oscillations and realize high-average power potential, a new lossy ceramic material with weak electric conductivity is loaded in the TE01 mode cylindrical interaction waveguide. The loss-free output taper is carefully optimized to suppress oscillations and maintain broadband amplification. Employing a magnetic injection gun of beam voltage 70 kV, beam current 3 A, pitch factor 1.5, and axial-velocity spread 5%, theoretical investigation predicts that the gyro-TWT amplifier is of excellent performance, which includes being driven to saturation with input power Pin <; 0.4 W, highest efficiency of 32.4%, and the bandwidth of 4.2 GHz with output power exceeding 50 kW.