This paper presents a flexible solid-state supercapacitor of high energy density. The electrodes of the supercapacitor are made of porous and absorbent cotton paper coated with single-wall carbon nanotubes. To ensure all solid-state configuration, a solid-state polymer-based electrolyte (poly (vinyl alcohol)/phosphoric acid) is used. The as-fabricated supercapacitor can be charged to over 3 V. It has high specific capacitance and high energy density of 115.8301 F/g carbon and 48.8587 Wh/kg carbon. Its performance is comparable to that of commercial supercapacitors, which need to utilize liquid electrolytes. Flexible solid-state supercapacitors offer several significant advantages for use in hybrid electric vehicles.