In this study, we report the fabrication of solid-state asymmetric supercapacitors (ASCs) based on conducting polymer electrodes on a plastic substrate. Nanostructured conducting polymers of poly(3,4-ethylenedioxythiophene), PEDOT, and polyaniline (PANI) are deposited electrochemically over Au-coated polyethylene naphthalate (PEN) plastic substrates. Due to the electron donating nature of the oxygen groups in the PEDOT, reduction potentials are higher, allowing it to be used as a negative electrode material. In addition, the high stability of PEDOT in its oxidised state makes it capable to exhibit electrochemical activity in a wide potential window. This can qualify PEDOT to be used as a negative electrode in fabricating asymmetric solid state supercapacitors with PANI as a positive electrode while employing polyvinyl alcohol (PVA)/H2SO4 gel electrolyte. The ASCs exhibit a maximum power density of 2.8 W cm−3 at an energy density of 9 mW h cm−3, which is superior to the carbonaceous and metal oxide based ASC solid state devices. Furthermore, the tandem configuration of asymmetric supercapacitors is shown to be capable of powering a red light emitting diode for about 1 minute after charging for 10 seconds.