A systematic theoretical and experimental study on 35 GHz 45KV third-harmonic gyrotron with a permanent magnet system is presented in this paper. A complex cavity with gradual transition, and a diode magnetron injection electron gun (MIG) are employed in the gyrotron. A self-consistent field nonlinear theoretical investigation and numerical simulation for electron beam interaction with RF fields are given. The diode MIG is simulated numerically utilizing our code in detail. The permanent magnet system provided the axial magnetic field of about 4.5KGs in the cavity region of the gyrotron. The Ka band third-harmonic complex cavity gyrotron with a permanent magnet system has been designed, constructed and tested. A peak output power of 146.3KW was obtained at a beam voltage of 45KV with beam current of 32.2A, corresponding to an efficiency of 10.2%.