Supercapacitors operating in aqueous solutions are low cost energy storage devices with high cycling stability and fast charging and discharging capabilities, but generally suffer from low energy densities. Here, we grow Ni(OH)2 nanoplates and RuO2 nanoparticles on high quality graphene sheets in order to maximize the specific capacitances of these materials. We then pair up a Ni(OH)2/graphene electrode with a RuO2/graphene electrode to afford a high performance asymmetrical supercapacitor with high energy and power density operating in aqueous solutions at a voltage of ~1.5 V. The asymmetrical supercapacitor exhibits significantly higher energy densities than symmetrical RuO2–RuO2 supercapacitors or asymmetrical supercapacitors based on either RuO2– carbon or Ni(OH)2–carbon electrode pairs. A high energy density of ~48 W•h/kg at a power density of ~0.23 kW/kg, and a high power density of ~21 kW/kg at an energy density of ~14 W•h/kg have been achieved with our Ni(OH)2/graphene and RuO2/graphene asymmetrical supercapacitor. Thus, pairing up metal-oxide/graphene and metal-hydroxide/graphene hybrid materials for asymmetrical supercapacitors represents a new approach to high performance energy storage.