Electric double-layer capacitors (DLCs) can have high storage capacity, but their porous electrodes cause them to perform like resistors in filter circuits that remove ripple from rectified direct current. We have demonstrated efficient filtering of 120-hertz current with DLCs with electrodes made from vertically oriented graphene nanosheets grown directly on metal current collectors. This design minimized electronic and ionic resistances and produced capacitors with RC time constants of less than 200 microseconds, in contrast with ~1 second for typical DLCs. Graphene nanosheets have a preponderance of exposed edge planes that greatly increases charge storage as compared with that of designs that rely on basal plane surfaces. Capacitors constructed with these electrodes could be smaller than the low-voltage aluminum electrolyte capacitors that are typically used in electronic devices.