Rogue-waves in gyrotrons represent sporadically emitted ultrashort electromagnetic pulses with intensities significantly greater than the average radiation power and, in optimal conditions, higher than the power of the driving electron beams. In this paper within the framework of the average approach and direct 3D PIC (particle-in-cell) simulations, we study the possibility of rogue wave generation in submillimeter-band gyrotrons operating at high-order modes. It is demonstrated that in a 500 GHz fundamental cyclotron harmonic gyrotron excited by the 30 kV/50 A helical electron beam the peak power of generated picosecond electromagnetic spikes at TE61 mode can reach 5 MW that more than three times exceeds the power of the driving beam.