The inherently large surface area and electrical conductivity of graphene-like electrodes have motivated extensive research for their use in supercapacitors. Although these properties are beneficial for the electric double layer (EDL) capacitance, the full utilization of graphene is curtailed by its intrinsically limited quantum capacitance due to the low density of electronic states near the neutrality point. While recent work has demonstrated that modifications to graphene can generally mitigate this limitation, a comprehensive analysis of the impact of graphene edges, which can be created during synthesis and post-treatment, has yet to be reported. Using a theoretical approach, we investigate the influence of graphene edges on both the quantum and EDL capacitances using edge-passivated zigzag graphene nanoribbons (ZGNRs) in [BMIM][PF6] ionic liquid as model systems. Our findings show that the presence of edges improves the quantum capacitance by increasing the electronic density of states, which is further amplified as the ZGNR width decreases. Our analysis also reveals that the EDL microstructure can be noticeably altered by the edges, which in turn increases the EDL capacitance. Through comparisons with pristine graphene electrodes, our study clearly highlights that edge defects in graphene-like electrodes can enhance supercapacitor performance by dramatically augmenting both EDL and quantum capacitances.