Abstract: To date, the simulation of the nonequlibrium phenomenon including chemical reacting in high-speed flows is still a challenging work. Based on the strategy of statistical mechanics, DSMC (Direct Simulating Monte Carlo) is believed to be an effective method in revealing the physic underlying the nonequlibrium phenomenon. Bird et al. pointed out that the number of molecules is an extremely important parameter in DSMC simulation, and an empirical value, approximately 20~30 in each calculation cell, was suggested in a general DSMC simulation without any thermal or chemical nonequilibrium phenomena. In this paper, a new factor considering the thermal and chemical nonequilibrium effects is proposed and examined in the DSMC simulation of the nitrogen-oxygen dissociation reaction flows under a hot bath environment. Results show that the number of molecules could significantly affect the accuracy in all of the simulations, and it is highly related with the specific physical problems. It suggests that the number of molecules in each calculation cell should be proportional to the local temperature and limited by a certain value in order to obtain a sufficiently accuracy results. On the other hand, the independence on the molecule number is identified with continues increasing the molecule number, which agrees with the theoretical analysis. Finally, with respect to the balance between the calculation cost and efficiency, several examined values in the present study are valuable for further references and are able to be regarded as canonical parameters in DSMC simulation.