Herein, we report the one-pot co-synthesis of a novel water-stable nickel-based metal-organic framework (Ni-MOF) with a Co-MOF, as well as the dual Ni/Co-MOF-reduced graphene oxide (rGO) nanocomposite in the same reaction vessel. Introduction of the two metal precursors along with the organic linker in the same reaction vessel guarantees in situ homogeneously distributed MOF particles in the nanoscale level that cannot be obtained by physical mixing of the MOFs synthesized individually. The Ni/Co-MOF-rGO nanocomposite demonstrates a high specific capacitance of 860 F/g at 1.0 A/g. The asymmetric activated carbon//Ni/Co-MOF-rGO device delivers specific energy of 72.8 Wh/kg at 850 W/kg, and still holds 15.1 Wh/kg under the high specific power of 42.5 kW/kg, as well as a long cycle life (91.6% capacitance retention after 6000 charge-discharge cycles at 1 A/g). Two 1.0 cm2 devices connected in series run a clock for about 2 h, and also sequentially power a blue light emitting diode (LED) for 25 min, then a green LED for 25 min, and finally a red LED for more than 140 min, demonstrating that the nanocomposite is a very promising active material for practical applications.