A three-dimensional numerical simulation of the starting process of a 94GHz gyrotron is carried out carefully, based on the theories of PIC and electron cyclotron resonance maser, while the TE6,2 mode is selected as the operating mode of the gyrotron. The parameters such as the beam voltage, beam current and beam radius of the guiding center are set according to the measured data of the 94 GHz gyrotron in the National Key Laboratory of Science and Technology on Vacuum Electronics. As a result, an output power of the operating mode of 84kW, corresponding to 33.5% efficiency and an oscillation frequency of 94 GHz have been achieved with the working magnetic field of 3.56Tesla. The output power is in good agreement with the experimental test results, which is also consistent with the calculation results using the stable beam wave interaction code established by us.