The density scaling of n = 1 error field penetration is investigated under radio-frequency (RF)-dominant heated L-mode discharges in the EAST tokamak. It is found that the density scaling of the threshold field strength for error field penetration in lower-hybrid current drive (LHCD) plasmas is about , where br represents the error field amplitude. The results show a weaker density dependence compared to that observed in the previous ohmic heated discharges (Wang et al 2018 Nucl. Fusion58 056024). For a better understanding of the density scaling, it is compared with field penetration theories, and it is found that it lies in the Waelbroeck regime. The observed scaling is consistent with that evaluated with the magnetohydrodynamic (MHD) theory on error field penetration, for which all the physical parameters are determined experimentally. Due to the density dependence of LHCD heating efficiency, the stronger negative correlation between density and temperature results in a weaker density scaling in these LHCD plasmas. Using realistic parameters under LHCD and ohmic heating as input, respectively, the numerical results based on a reduced MHD model reproduce well the scaling from the error field penetration theory and the observations. Besides, the density scaling in various tokamak operational regimes is also numerically investigated. This provides an excellent validation of MHD theory on error field penetration in the RF-dominant heated L-mode discharges.