In this article, we described about the preparation and electrochemical properties of a flexible energy storage system based on a plastic polyethylene terephthalate (PET) substrate. The PET treated with UV/ozone was fabricated with multilayer films composed of 30 polyaniline (PANi)/graphene oxide (GO) bilayers using layer-by-layer assembly of positively charged PANi and negatively charged GO. The conversion of GO to the reduced graphene oxide (RGO) in the multilayer film was achieved using hydroiodic acid vapor at $100^{circ}C$, whereby PANi structure remained nearly unchanged except a little reduction of doping state. Cyclic voltammetry and charge/discharge curves of 30 PANi/RGO bilayers on PET substrate (shorten to PANi-$RGO_{30}$/PET) exhibited an excellent volumetric capacitance, good cycling stability, and rapid charge/discharge rates despite no use of any metal current collectors. The specific capacitance from charge/discharge curve of the PANi-$RGO_{30}$/PET electrode was found to be $529F/cm^3$ at a current density of $3A/cm^3$, which is one of the best values yet achieved among carbon-based materials including conducting polymers. Furthermore, the intrinsic electrical resistance of the PANi-$RGO_{30}$/PET electrodes varied within 20% range during 200 bending cycles at a fixed bend radius of 2.2 mm, indicating the increase in their flexibility by a factor of 225 compared with the ITO/PET electrode.