Edge localized modes (ELMs) are completely suppressed by ion cyclotron resonant heating (ICRH) during H-mode discharge, which is first observed in the Experimental Advanced Superconducting Tokamak (EAST). The electromagnetic turbulence model in the BOUT++ framework is applied to the simulations, with the aim of obtaining the key physics mechanisms of ELM suppression by ICRH. The simulations, for the EAST experiment with no ELMs after ICRH, reveal that the radio frequency (RF) sheath plays a key role in the suppression of ELMs. The simulation results show that: (a) using the flow-balanced electric field, the ELM sizes are about 3.4% before ICRH, and 2.1% after ICRH. Although the smaller ELM is obtained with ICRH, it still belongs to relatively large ELMs; (b) instead of the flow-balance condition, the radial electric field Er is calculated using the RF sheath model, and the ELM size is about 0.36% with ICRH, much closer to the small/no ELM regime. After considering the effect of ICRH, the larger E × B shear rate in the pedestal and scrape-off layer induced by the RF sheath reduces the linear growth rate, and enhances the nonlinear mode coupling. Furthermore, we find that there is an effective range of the sheath potential, in which the ELM can be well suppressed, but beyond this range the ELM may be only mitigated rather than suppressed. This can reasonably explain why the probability of ELM suppression by ICRH appearing in the experiments is low.