Coincident study on the intensity change of the ground cosmic rays during thunderstorms is very important for understanding the acceleration mechanism of secondary charged particles caused by atmospheric electric field. It is found that the strength of the near earth thunderstorm electric field can be up to 1000 V/cm or even higher from ARGO-YBJ (where YBJ stands for Yangbajing, 4300 m a.s.l., Tibet, China) data in 2012. In this paper, Monte Carlo simulations are performed by using CORSIKA program to study the correlations between the intensity of the ground cosmic rays and the near earth thunderstorm electric field at YBJ. When the atmospheric electric field strength is higher than the threshold field strength (ERB) for the development of a runaway breakdown process, the total number of electrons and positrons is exponentially increases. At an electric field strength of 1500 V/cm, the number increases exponentially and reaches a maximum value at an atmospheric depth of ～520 g/cm2, where the electric field is slightly stronger than the threshold field strength. These results are consistent with the theoretical results of relativistic runaway electron avalanche (RREA) which was proposed by Gurevich et al. () and also supports Dwyer's theory. The total number of electrons and positrons increases with the strength of the field in the negative field or in the positive field greater than 600 V/cm, while a certain degree of decline occurs in the positive field less than 400 V/cm. In the range 400-600 V/cm, the energy of the primary proton should be taken into account. For the primary energy that is lower than 80 GeV, the total number of electrons and positrons increases. And it does not change obviously when the energy is between 80 GeV and 120 GeV. For the primary energy exceeds 120 GeV, the number drops off, and the decrease is of ～4%. During thunderstorms, a short duration occurs in which the single particle counting rate increases as energy lowers, while a decrease happens with energy becoming higher than that from ARGO-YBJ data. Our preliminary results can give reasonable explanations to the experimental observations of ARGO-YBJ.