A design of a cryomagnet-based second-harmonic gyrotron is proposed, in which a special profile of an axisymmet-ric cavity is used for efficient discrimination of the fundamental-harmonic mode in a wide range of operating magnetic fields and for providing a wide band of the frequency tuning when operating in several axial modes. According to simulations, for the beam voltage of 15 kV it is possible to achieve a frequency tuning of up to 0.3% when operating at several axial modes near the frequency of 400 GHz with an output power of at least 10 W. This design is to be implemented on the base of 8 T cryomagnet at the FIR Center, Fukui.