Sodium ion capacitors (SICs) are designed to deliver both high energy and power densities at low cost. Electric double-layer capacitive cathodes are typically used in these devices, but they lead to very limited capacity. Herein, we apply a pseudocapacitive layered ferric vanadate (Fe-V-O) as cathode to construct non-aqueous SICs with both high energy and power densities. The Fe-V-O nanosheets cathode displays remarkable rate capability and cycling stability. The pseudocapacitive sodium storage mechanism of Fe-V-O, with over 83% of total capacity from capacitive contribution, is confirmed by kinetics analysis and ex situ characterizations. The capacitive-adsorption mechanism of hard carbon (HC) anode is demonstrated, and it delivers excellent rate capability. Based on as-synthesized materials, the assembled HC//Fe-V-O SIC delivers a maximum energy density of 194 Wh kg^-1 and power density of 3,942 W kg^-1. Our work highlights the advantages of pseudocapacitive cathodes for achieving both high energy and power densities in sodium storage devices.