Abstract: This article mainly designs a field emission cold cathode electron gun using a hexagonal pyramid embedded cylindrical cathode structure. The anode current and focal size of the electron gun are simulated using Computer Simulation Technology particle studio software, and the structure of the electron gun is continuously optimized. Finally, a dual focusing electrode dual grid electron gun with an effective focal size of about 20 μm, anode current of 3.8 mA, and electron pass rate of 84.5% is designed. In addition, simulation results showed that in the dual-focusing electrode structure electron gun, the V_f1/V_f2 at which the electron gun obtains the minimum focal size decreases with increasing V_f2. At the same time, the anode current increases with increasing V_f1/V_f2, and this increase significantly expands with increasing V_f2. These findings provide important guidance for further optimizing the performance of the electron gun.