High-rate electrochemical hybrid supercapacitors (HSCs) have attracted great scientific attention due to the expectation of the battery-level energy density and super long life as electrochemical double-layer capacitors. But in reality, the rational design of HSCs with a balanced capacity of positive and negative electrodes with high-rate capability is still a great challenge. Herein, a unique strategy is applied by pairing the binder-free NiCo2O4 ultrathin nanosheets supported on carbon fiber paper (Ni-Co-O@CFP) as cathode and metal-organic-framework (MOF) derived nanoporous nitrogen-doped carbon nanosheets (NPC) as an anode to fabricate the hybrid supercapacitor (NCO parallel to NPC-HSC). The specific capacitance of the Ni-Co-O@CFP electrode reaches 2038 F g(-1) (339 mAh g(-1)) at 1.5 A g(-1) with capacitance retention of 93.65% after 5000 charge-discharge cycles at a high current density of 20 A g(-1). The as-fabricated NCO parallel to NPC-HSC exhibited excellent electrochemical properties in PVA/KOH hydrogel electrolyte with highly flexible characteristics. The NCO parallel to NPC-HSC can work under the extended potential window of 0.0-1.6 V and reach at a high specific capacitance of 201 F g(-1) at 0.55 A g(-1), providing ultra-high energy density of 69 Wh kg(-1) at a power density of 840 W/kg, which is substantially higher than values reported for symmetric and asymmetric supercapacitors based on the NiCo2O4 till date. Moreover, the NCO parallel to NPC-HSC demonstrated the negligible change in performance while bent at different states. Overall, our NCO parallel to NPC-HSC exhibits exceptionally good cycling performance over 20,000 cycles (>90% capacitance retention). Interestingly, three NCO parallel to NPC-HSC devices connected in series can power 16 green color light-emitting-diodes (LEDs, 2 V) for more than 2 min, demonstrating its fusibility as a practical energy storage device. (c) 2020 Elsevier Ltd. All rights reserved.