A solid-state supercapacitor with a flexible, simple structure based on graphene thin film electrodes and acid/base/salt–PVA gel electrolytes is reported. The performance of six different gel electrolytes (H3PO4, H2SO4, KOH, NaOH, KCl, NaCl) in this graphene-based supercapacitor are investigated. The electrochemical properties of this highly flexible, stable supercapacitor are enhanced by optimizing the concentration of the electrolyte in polymer gel.