In order to develop millimeter wave electric vacuum radiation source devices with field emission cold cathodes, the electron-optical system using a large area carbon nanotube cold cathode (CNCC) was investigated, which can generate an electron beam with large current and high current density. By adding a mesh grid on the cathode surface of a Pierce electron gun, problems of the electron bunching and high electric field applied to the CNCC surface have been solved. Based on the experimental results of a CNCC, the field emission model was built, by using PIC simulation software, to simulate the Pierce electron-optical system. The effect of the mesh grid on the electron beam has been analyzed. And the influence of the anode voltage and the axial magnetic field for the electron beam radius has been researched. The simulation results of the electron-optical system showed that when the area of cathode is 3.03 cm2, an electron beam with 210 mA at 60 kV can be produced. The current density is 6.7 A/cm2 and the maximum radius of the electron beam is 1 mm.