Electrochemical batteries and capacitors are important devices for electrical energy storage with wide applications from portable electronics to transportation, and to grid.  However, rechargeable batteries are typically limited in poor power density, while supercapacitors deliver low energy density.  One “Holy Grail” of energy storage is to have an energy density up to the level of Li-ion batteries and a power density and cycling life identical to supercapacitors.  Here we design a novel symmetric Na-ion pseudocapacitor with a power density exceeding 5.4 kW/kg at 11.7 A/g, a cycling life retention of 64.5% after 10,000 cycles at 1.17 A/g, and an energy density of 26 Wh/kg at 0.585 A/g.  Such a device operates on oxidation-reduction reactions occurring on both electrodes with an identical active material, viz., Na₃V₂(PO₄)₃ encapsulated inside nanoporous carbon.  This device, in a full-cell scale utilizing highly reversible, high-rate, cost-effective Na-ion intercalational pseudocapacitance, can bridge the performance gap between batteries and supercapacitors.  The characteristics of the device and the potentially low-cost production make it attractive for hybrid electric vehicles and low maintenance energy storage system.