Since to break the limitation of traditional single anode magnetron injection electron gun can only produce a lower power, this paper, based on an independent research and development of particle simulation software CHIPIC, will take the 110 GHz, 220 GHz coaxial cavity double-beam gyrotron for full three-dimensional numerical simulation study. By theoretical analysis for the initial parameters of the coaxial double-beam electron gun and to optimize the design by CHIPIC, we obtain the high-performance electron beam with the horizontal and vertical velocity ratio of 1.0 and the maximum velocity spread of 5.4%, and use the optimized electron gun to replace the traditional gyrotron emission for numerical simulation of the 110 GHz, 220 GHz gyrotron system, as well as the four-process parallel MPI in computing. Finally we obtain that the double bands are 110 and 220 GHz respectively, a TE02 mode, and the average output power about 70 kW. The efficiency can reach 8.75% for the high performance double-beam gyrotron oscillating tube.