A cylindrical gyrotron cavity is designed and optimized with a high order mode TE34,10-to deliver an output power of megawatts level at 140 GHz. Analysis on mode competition indicates that the two adjacent modes TE33,10-and TE31,11+ involve in competition and cause significant decreasing of output power of TE34,10-. To suppress the competition hysteresis loops of TE31,11+ and TE33,10-with TE34,10-are calculated, which indicates TE34,10-can inhibit growth of the other two modes with decreasing magnetic field from its low efficiency single mode oscillation zone, while it turned out just the opposite with increasing magnetic field due to the earlier oscillation of the competitors. Based on the results, a multimode time-dependent calculation including 42 modes is carried out with magnetic field dropping from 5.59 T to 5.51 T, the results show that mode competition is successfully suppressed, the operation mode TE34,10-realizes stable single mode oscillation with an output power of 0.96 MW and an electron efficiency of 36.7% at 140 GHz.