Combining high-capacitive metal oxides and excellent conductive carbon substrates is a very significant strategy to achieve high-performance electrodes for electrochemical capacitors (ECs). Herein, the bimetallic (Ni, Co) hydroxide is uniformly grown on the electro-etched carbon cloth (CC) by a facile co-electrodeposition method, and then the honeycomb-shaped NiCo₂O₄/CC (HSNC) composite is formed by transforming the hydroxide precursor into its bimetallic oxides through the subsequent thermal treatment. The special structure of the HSNC as binder-free electrode is responsible for its excellent electrochemical performance with carbon-like power feature. The experimental results show that HSNC electrode exhibits a high specific capacitance with remarkable cycle stability (94.3% after 10 000 cycles at 10 A g⁻¹) in the three-electrode configuration. To evaluate further the capacitive performance of the as-prepared binder-free electrode in a full cell set-up, an asymmetric electrochemical capacitor (AEC) is assembled by using the HSNC as the positive electrode and reduced graphene oxide/carbon cloth (rGO/CC) as the negative electrode in KOH electrolyte. The as-assembled device presents an energy density as high as 32.4 W h kg⁻¹ along with power density of 0.75 kW kg⁻¹, comparing with nickel-metal hyoride battery (Ni-MH) batteries (30.0 W h kg⁻¹ at 0.35 kW kg⁻¹). Even at the power density of 37.7 kW kg⁻¹ (50-time increase, a full charge–discharge within 3.5 s), energy density still holds at 17.8 W h kg⁻¹, indicating an outstanding rate capability. Furthermore, the as-fabricated device exhibits a long cycle lifetime (76.5% after 10 000 cycles at 3 A g⁻¹) with a cell voltage of 1.5 V.