Abstract: The phenomenon of multipactor discharge suppressing on the grooved dielectric surfaceadopted in experiment is simulated with the Monte Carlo method. Dynamic equations, grooved surface boundary, initial energy and angular distribution of secondary electrons, and the secondary electron emission ratio are introduced. The suppressing effect of multipactor discharge depending on the depth and width of the groove is discussed. In addition, the suppressing ability of multipactor discharge on a fixed grooved surface depending on electric field and frequency of microwave is studied. Finally, the avoidance of two-sided multipactor discharge on the grooved surface is put forward. The numerical results are as follows: increasing groove depth and decreasing groove width could improve suppressing ability of multipactor discharge;it could be easy to suppress high frequency and weak or high electric field of microwave for a fixed grooved surface structure;it is necessary for avoiding the region of two-sided multipactor discharge. The numerical results agree with relevant experimental phenomena.