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Mode conversion of high-power electromagnetic microwave (HPEM) was successfully accomplished using a coaxial-beam rotating antenna (COBRA) in an X-band relativistic backward-wave oscillator (RBWO). The mode conversion from the TM01 mode to the circularly polarized TE11-likeness mode was identified by both cold test and hot test. To observe whether mode conversion is effective or not, the radiation pattern of TE11-likeness mode by COBRA lens was compared with the case of the radiation pattern of TM01 mode using simple horn antenna. Their radiation patterns could be described by fluorescent lamps. The experimental results of radiation pattern measurements are shown to be in a reasonable agreement with the simulated one. The maximum value of RF output power appeared at the center of COBRA lens from the experimental results.