We report on the molecular dynamics simulations of the electrical double layers (EDLs) at the interface of ionic liquids [BMIM][NO3] and planar electrodes. Simulations confirm that a Helmholtz-like interfacial counterion layer exists when the electrode charge density is negative or strongly positive, but the counterion layer is not well-defined when the electrode charge density is weakly positive. The thickness of the EDL, as inferred from how deep the charge separation and orientational ordering of the ions penetrate into the bulk ILs, is about 1.1 nm. The liquid nature of the IL and the short-range ion−electrode and ion−ion interactions are found to significantly affect the structure of the EDL, particularly at low electrode charge densities. Charge delocalization of the ions is found to affect the mean force experienced by the ions and, thus, can play an important role in shaping the EDL structure. The differential capacitance of the EDLs is found to be nearly constant under negative electrode polarization but increases dramatically with the potential under positive electrode polarization. We show that the differential capacitance is a quantitative measure of the response of the EDL structure to a change in electrode charge density. It is found that the [NO3]− ion dominates the response of EDL structure to the change in electrode charge under both positive and negative electrode polarization, which is qualitatively different from that in aqueous electrolytes. Detailed analysis shows that the cation−anion correlations and the strong adsorption of [BMIM]+ ions on the electrode are responsible for the capacitance−potential correlation observed here.