Recent experiments have revealed that onion-like carbons (OLCs) offer high energy density and charging/discharging rates when used as the electrodes in supercapacitors. To understand the physical origin of this phenomenon, molecular dynamics simulations were performed for a room-temperature ionic liquid near idealized spherical OLCs with radii ranging from 0.356 to 1.223 nm. We find that the surface charge density increases almost linearly with the potential applied on electric double layers (EDLs) near OLCs. This leads to a nearly flat shape of the differential capacitance versus the potential, unlike the bell or camel shape observed on planar electrodes. Moreover, our simulations reveal that the capacitance of EDLs on OLCs increases with the curvature or as the OLC size decreases, in agreement with experimental observations. The curvature effect is explained by dominance of charge overscreening over a wide potential range and increased ion density per unit area of electrode surface as the OLC becomes smaller.