We use a mean field model for ionic liquids, which takes into account both the ion correlation and the finite ion size effects, in order to calculate the differential capacitance of the ionic liquid interface with single-layer graphene. Besides choosing ion packing fractions that give rise to the camel-shaped and bell-shaped capacitances of the diffuse layer in ionic liquids, we also explore small packing fractions in the regime of "dilute electrolytes", as well as different packing fractions for different ion species in asymmetric ionic liquids. We find that the main effect of a graphene electrode arises due to a V-shaped minimum in its quantum capacitance at the point of zero charge (PZC), which is a manifestation of the Dirac cone structure of graphene's pi electron bands. As a result, the total capacitance of a graphene -ionic liquid interface exhibits a camel-shaped dependence on the total applied potential, even for large ion packing fractions and finite ion correlation lengths. While the minimum at the PZC in the total capacitance is "inherited" from graphene's quantum capacitance, the two peaks that occur for applied potentials similar to +/- 1 V are sensitive to the presence of the ion correlation and a Stern layer, which both tend to reduce the height and flatten the peaks in the camel-shaped total capacitance. Finally, we have found that the largest fraction of the applied potential goes to charging the graphene electrode. (C) 2019 Elsevier Ltd. All rights reserved.