The Large High Altitude Air Shower Observatory (LHAASO) has three sub-arrays, KM2A, WCDA, and WFCTA. As the major array of LHAASO, KM2A has been operating stably in shower mode. To study the near-earth atmospheric electric field (AEF) effect on the trigger event rate during thunderstorm, Monte Carlo simulations are performed with CORSIKA and G4KM2A. According to the simulations, the shower rate variations are found to be strongly dependent on the strength and polarity of the AEF. The shower rates increase and the variations become larger with the field intensity. In positive AEF (defined as the direction pointing towards the ground), the increased amplitude is less than that in negative AEF. With the same field strength 1000 V/cm, the value exceeds 12% in negative field, and merely is up to 6% in positive one. The dependence of the trigger rate variation on the thickness of AEF layer is also simulated. The shower event rate increases dramatically at small thickness, and then the curve flattens out. This indicates that the AEF with larger layer thickness has more deflection effects on the development of extensive air shower. The shower rate variations are also found to be dependent on the primary zenith angles. Our simulation results could be useful in understanding the variation of trigger rate detected by LHAASO-KM2A during thunderstorms.