The combination of layered nanorod arrays with unique core–shell structure and transition metal layered double hydroxide (LDH) is considered as a feasible solution to improve the electrochemical performances of capacitor electrode. In this study, layered ZnNiFe-LDH@Cu(OH)2/CF core–shell nanorod arrays, which consist of ultrathin ZnNiFe-LDHs nanosheet shells and ordered Cu(OH)2 nanorod inner cores, are successfully designed and fabricated by a typical hydrothermal way and a simple in situ oxidation reaction. The electrode prepared using ZnNiFe-LDH@Cu(OH)2/CF nanomaterial reveals an remarkable area capacitance of 6100 mF cm−2 at 3 mA cm−2 current density, which is excellently superior than those of ZnFe-LDH@Cu(OH)2/CF, NiFe-LDH@Cu(OH)2/CF, Cu(OH)2/CF and CF. Additionally, the capacitance retention remains as high as 83.4% after 5000 cycles and a very small Rs (0.567 Ω) can be observed. In addition, an asymmetric supercapacitor device is successfully fabricated employing ZnNiFe-LDH@Cu(OH)2/CF. Meanwhile, the ZnNiFe-LDH@Cu(OH)2/CF//AC device can achieve an energy density of 44 Wh kg−1 and a corresponding power density of 720 W kg−1 and possess the capability to light up a multi-function monitor for 33 min just using two ASC equipments connected in series. Therefore, the prepared ZnNiFe-LDH@Cu(OH)2/CF composite materials with unique structure has great application potential in energy storage devices.