The two-stage tapered gyro-TWT has shown its stable operation at Ka-band with 20% bandwidth. A Ka-band harmonic multiplying amplifier is being investigated employing an axis-encircling electron gun with moderate beam voltage of 30 kV and current of 1A. A two-stage linearly tapered interaction circuit is chosen using a rectangular waveguide. A nonlinear simulation predicted a saturated gain of 25 dB with peak power of 4 kW without axial velocity spread of electron beam at the third harmonic. The bandwidth of 9% is predicted at the center frequency of 35 GHz. The bandwidth decreases to 3% when the velocity spread of 4% is assumed. A detailed discussion on the design will be presented.