High-rate asymmetric supercapacitors (ASCs) made of abundant and low-cost electrode materials and operating in safe aqueous electrolytes could be attractive for electrochemical energy storage. Here, we design a new type of ASC by using pseudo-capacitive nanomaterials, Ni-Co double hydroxide (Ni-Co DH) nanosheets and polypyrrole (PPy) film, for cathode and anode, respectively which were integrated with functionalized partial-exfoliated graphite (FEG) current collector.Benefiting from the "super highway" for fast electron/ion transportation in the hybrid systems, the as-prepared electrodes exhibit superior rate capability (2442 and 2039 F/g at 1 and 50 A/g, with 83.5% retention for Ni-Co DH; 560 and 441 F/g at 1 and 50 A/g, with 79% retention for PPy). The assembled ASC displays a high specific capacitance (261 F/g at 1 A/g) and excellent rate capability, 77% of its initial capacitance can be retained when the current density increases 30 times from 1 to 30 A/g. An energy density of 61.3 Wh/kg can be achieved by the ASC at 0.65 kW/kg. Even at an ultra-high power density of 19.5 kW/kg, the ASC can still deliver a high energy density of 47.2 Wh/kg. Through careful control of charges which can be stored in anode and cathode, cycling stability of the ASC is much improved, 91% capacitance retention can be achieved after 5000 charge-discharge cycles. These features demonstrate a new avenue for developing high-performance pseudocapacitive electrodes and rational assembly strategies for high power/energy density charge storage devices with good cycling stability.A high-rate asymmetric supercapacitor (ASC) was developped by employing high rate pseudo-capacitive nanomaterial/graphene hybrid electrode for both electrodes.