A novel type of frequency doubling gyrotron traveling wave amplifier (FD-GTWT) for applications that require high-power microwave in the sub-THz frequency range is presented. The proposed FD-GTWT delivers high power and high gain over a broad bandwidth and simultaneously doubling the frequency of the input signal. Simulations of a first 263 GHz FD-GTWT design are presented, which show for a 10 mW driving signal at 131.5 GHz an RF output power of 250 W at 263 GHz and a gain of >40 dB over a bandwidth of 17.5 GHz. The basis of the FD-GTWT are two interaction circuits separated by a long drift section. In the first circuit, the electron beam is pre-bunched at the fundamental cyclotron harmonic. In the second one, highpower RF is induced by the pre-bunched electron beam at the 2nd cyclotron harmonic. Both sections consist of helically corrugated waveguides that efficiently suppress parasitic interactions and allow broad bandwidth.