Design of new materials with sophisticated nanostructure has been proven to be an efficient strategy to improve their properties in many applications. Herein, we demonstrate the successful combination of high electron conductive materials of NiCo2O4 with high capacitance materials of MnMoO4 by forming a core-shell nanostructure. The NiCo2O4@MnMoO4 core-shell nanoarrays (CSNAs) electrode possesses high capacitance of 1169 F g-1 (4.24 F cm-2) at a current density of 2.5 mA cm-2, obviously larger than the pristine NiCo2O4 electrode. The asymmetric supercapacitors (ASCs), assembled with NiCo2O4@MnMoO4 CSNAs as binder-free cathode and active carbon (AC) as anode, exhibit high energy density of 15 Wh kg-1 and high power density of 6734 W kg-1. Cycle performance of NiCo2O4@MnMoO4 CSNAs//AC ASCs, conducted at current density of 20 mA cm-2, remain 96.45% of the initial capacitance after 10,000 cycles, demonstrating its excellent long-term cycle stability. Kinetically decoupled analysis reveals that the capacitive capacitance is dominant in the total capacitance of NiCo2O4@MnMoO4 CSNAs electrode, which may be the reason for ultra long cycle stability of ASCs. Our assembled button ASC can easily light up a red LED for 30 min and a green LED for 10 min after being charged for 30 s. The remarkable electrochemical performance of NiCo2O4@MnMoO4 CSNAs//AC ASCs is attributed to its enhanced surface area, abundant electroactive sites, facile electrolyte infiltration into the 3D NiCo2O4@MnMnO4 nanoarrays and fast electron and ion transport path.