Summary form only given. To achieve high power millimeter waves at Ka-band, a harmonic-multiplying gyro-TWT is developed. The designed interaction circuit is a 2-stage waveguide that consists of input and output sections divided by severing. Both stages are linearly tapered rectangular waveguides in which the fundamental TE10 mode is used. Tapering the waveguides increases stabilities and bandwidth by distributed interaction when the grazing condition along the taper is satisfied. In this study, each stage employs X-band and Ka-band frequencies, respectively. Through the fundamental and the 3rd electron cyclotron harmonics at each stage, a harmonic-multiplying interaction occurs. As a result, a saturated gain of 23 dB, an electronic efficiency of 10%, and a bandwidth of 3% were predicted by a self-consistent nonlinear calculation on the assumption of 4% axial velocity spreads of electrons when an axis-encircling electron gun at a moderate beam voltage of 30 kV and a current of 1 A is employed.