In EAST, the phenomenon that the edge localized modes (ELMs) are effectively controlled by the low-hybrid waves (LHW) heating has been observed, including mitigating, suppressing, and triggering. Previous studies have shown that the ELM mitigation is mainly due to the formation of helical current filaments (HCFs) in the scrape-off layer (SOL) induced by LHW (Liang et al 2013 Phys. Rev. Lett.110 235002). However, the nonlinear interaction between HCF and ELMs remains unclear. To analyze the influence of HCF on ELMs, the numerical simulations are carried out using the BOUT++ framework. The six-field two-fluid model is modified to introduce an imposed current as the HCF. The simulations reveal that the magnetic flutter induced by HCF is the key factor in the ELM mitigation. The results indicate that: (1) the ELM size is 6.46% without HCF, while 3.88% with HCF. After considering the HCF effects, the ELM mitigation by LHW is reproduced, and the ELM energy loss is reduced by about 40%. HCF can decrease the growth rate and enhance the mode coupling. The energy inverse cascade is constrained by HCF, which leads to the absence of dominant filamentary structures and the mitigation of ELM; (2) with HCF, the heat flux on the divertor is effectively reduced, and the SOL width is broadened. HCF can significantly change the edge magnetic topology, which is beneficial for restricting the pedestal turbulence. The strike-point splitting of the particle flux is also reproduced in the simulations. In addition, through the parameter scanning, there is a window of the magnetic flutter δB/B induced by HCF, in which the ELM can be effectively mitigated. Meanwhile, the corresponding separatrix density window is presented, which can facilitate the ELM control by LHW more effectively.