We report detailed simulation results on the formation dynamics of an electrical double layer (EDL) inside an electrochemical cell featuring room-temperature ionic liquids (RTILs) enclosed between two planar electrodes. Under relatively small charging currents, the evolution of cell potential from molecular dynamics (MD) simulations during charging can be suitably predicted by the Landau–Ginzburg-type continuum model proposed recently (Bazant et al 2011 Phys. Rev. Lett. 106 046102). Under very large charging currents, the cell potential from MD simulations shows pronounced oscillation during the initial stage of charging, a feature not captured by the continuum model. Such oscillation originates from the sequential growth of the ionic space charge layers near the electrode surface. This allows the evolution of EDLs in RTILs with time, an atomistic process difficult to visualize experimentally, to be studied by analyzing the cell potential under constant-current charging conditions. While the continuum model cannot predict the potential oscillation under such far-from-equilibrium charging conditions, it can nevertheless qualitatively capture the growth of cell potential during the later stage of charging. Improving the continuum model by introducing frequency-dependent dielectric constant and density-dependent ion diffusion coefficients may help to further extend the applicability of the model. The evolution of ion density profiles is also compared between the MD and the continuum model, showing good agreement.