A nickel-functionalized copper metal–organic framework (Ni@Cu-MOF) was prepared by a facile volatilization method and a post-modification synthesis method at room temperature. The obtained Ni@Cu-MOF electrode delivered a high capacitance of 526 F/g at 1 A/g and had a long-term cycling stability (80% retention after 1200 cycles at 1 A/g) in a 6 M KOH aqueous solution. Furthermore, an asymmetric supercapacitor device was assembled from this Ni@Cu-MOF and activated carbon electrodes. The fabricated supercapacitor delivered a high capacitance of 48.7 F/g at 1 A/g and a high energy density of 17.3 Wh/kg at a power density of 798.5 kW/kg. This study indicates that the Ni@Cu-MOF has great potential for supercapacitor applications.