Design of a three-cavity Ka-band MW-level gyroklystron operated at the fundamental TE02 mode is presented in this paper. The initial design of the magnetron injection gun (MIG) and interaction circuit has been completed by using the PIC (Particle in cell) code MAGIC. The PIC simulation shows this gyroklystron can deliver an output power of more than 1.5 MW with a gain of > 35 dB at 36 GHz. The achieved efficiency exceeds 40 % when driven by a 95 kV, 45 A beam. The optimized MIG has a transverse velocity spread of less than 2.5% when the velocity ratio is around 1.3

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