Fabricating hierarchical core-shell nanostructures is currently the subject of intensive research in the electrochemical field owing to the hopes it raises for making efficient electrodes for high-performance supercapacitors. Here, we develop a simple and cost-effective approach to prepare CuO@MnO2 core-shell nanostructures without any surfactants and report their applications as electrodes for supercapacitors. An asymmetric supercapacitor with CuO@MnO2 core-shell nanostructure as the positive electrode and activated microwave exfoliated graphite oxide (MEGO) as the negative electrode yields an energy density of 22.1 Wh kg(-1) and a maximum power density of 85.6 kW kg(-1); the device shows a long-term cycling stability which retains 101.5% of its initial capacitance even after 10000 cycles. Such a facile strategy to fabricate the hierarchical CuO@MnO2 core-shell nanostructure with significantly improved functionalities opens up a novel avenue to design electrode materials on demand for high-performance supercapacitor applications.