Clinotron is a modification of the backward-wave oscillator. In clinotron the electron beam is inclined to slow wave structure (SWS). Due to the inclined electron beam, electrons are closer to SWS and can interact with stronger electric field, which leads to a higher output power and interaction efficiency. In this paper, the interaction system of clinotron is designed, and the double corrugated waveguide SWS is applied in clinotron for the first time. The dispersion curves, field distribution and beam-wave interaction are simulated with electromagnetic codes and 3D PIC codes. The result shows that more than 100 mW output power and a 50 GHz tuning bandwidth can be obtained. The simulation results show that the maximum output power is 2.3 W at frequency of 370.5 GHz with beam voltage 7.0 kV, beam current 120 mA and guiding magnetic field of 1.0 T.