In this study, a hierarchical ZnCo₂O₄@MnO₂ core–shell nanotube arrays electrode was developed by a facile two-step method. The electrode exhibits high specific capacitance of 1981 F g⁻¹ (2.38 F cm⁻²) at a current density of 5 A g⁻¹ and excellent cycling stability (5000 cycles). Furthermore, a low-cost, high-performance asymmetric supercapacitor (ASC) with ZnCo₂O₄@MnO₂ core–shell nanotube arrays on Ni foam (as positive electrode) and 3D porous α-Fe₂O₃ on Fe foil (as negative electrode) was successfully designed. The as-designed ASC device with an extended operating voltage window of 1.3 V achieved a specific capacitance of 161 F g⁻¹ at 2.5 mA cm⁻² with a maximum energy density of 37.8 W h kg⁻¹ and excellent stability with a capacitance retention of 91% after 5000 cycles. Furthermore, after being charged for dozens of seconds, the ZnCo₂O₄@MnO₂//α-Fe₂O₃-ASC can easily light up a LED. These fascinating performances indicate that the present ZnCo₂O₄@MnO₂ core–shell nanotube arrays with remarkable electrochemical properties could be considered as potential electrode materials for next generation supercapacitors in high energy density storage systems.