Clever and rational design of structural hierarchy, along with precise component adjustment, holds profound significance for the construction of high‐performance supercapacitor electrode materials. In this study, a binder‐free self‐supported CCO@N0.5C0.5OH/NF cathode material is constructed with hierarchical hetero‐core–shell honeycomb nanostructure by first growing CuCo2O4 (CCO) nanopin arrays uniformly on highly conductive nickel foam (NF) substrate, and then anchoring Ni0.5Co0.5(OH)2 (N0.5C0.5OH) bimetallic hydroxide nanosheet arrays on the CCO nanopin arrays by adjusting the molar ratio of Ni(OH)2 and Co(OH)2. The constructed CCO@N0.5C0.5OH/NF electrode material showcases a wealth of multivalent metal ions and mesopores, along with good electrical conductivity, excellent electrochemical reaction rates, and robust long‐term performance (capacitance retention rate of 87.2%). The CCO@N0.5C0.5OH/NF electrode, benefiting from the hierarchical structure of the material and the exceptional synergy between multiple components, demonstrates an excellent specific capacitance (2553.6 F g−1 at 1 A g−1). Furthermore, the assembled asymmetric CCO@N0.5C0.5OH/NF//AC/NF supercapacitor demonstrates a high energy density (70.1 Wh kg−1 at 850 W kg−1), and maintains robust capacitance cycling stability performance (83.7%) after undergoing 10 000 successive charges and discharges. It is noteworthy that the assembled supercapacitor exhibits an operating voltage (1.7 V) that is well above the theoretical value (1.5 V).