Tailor-made edge site-enriched inorganics coupled graphene hybrids hold a promising platform material for high-performance supercapacitors. Herein, we report a simple strategy for fabricating edge site-enriched nickel-cobalt sulfide (Ni-Co-S) nanoparticles decorated on graphene frameworks to form integrated hybrid architectures (Ni-Co-S/G) via an in situ chemically converted method. The Kirkendall effect-involved anion exchange reaction, e.g. the etching-like effort of the S2- ions, plays a crucial role for the formation of the edge site-enriched nanostructure. Density functional theory (DFT) calculations reveal that the Ni-Co-S edge sites have a high electrochemical activity and strong affinity for OH- in the electrolyte, which are responsible for the enhanced electrochemical performance. Benefiting from the integrated structures of Ni-Co-S nanoparticles and conductive graphene substrates, the resultant Ni-Co-S/G hybrid electrodes exhibit a high specific capacitance of 1492 F g-1 at the current density of 1 A g-1, a superior rate capability of 96% when the current density is increased to 50 A g-1, and excellent electrochemical stabilities. An asymmetric supercapacitor fabricated using the edge site-enriched Ni-Co-S/G hybrids as the positive electrode and porous carbon nanosheets (PCNS) as negative electrodes shows a high energy density of 43.3 W h kg-1 at a power density of 0.8 kW kg-1, and an energy density of 28.4 W h kg-1 can be retained even at a high power density of 22.1 kW kg-1.