Electrochemical double layer supercapacitor cells were fabricated and tested using composite electrodes of activated carbon with carbon black and poly(3,4-ethylenedioxythiophene) (PEDOT), and an organic electrolyte 1M TEABF4/PC solution. The effect of PEDOT on the performance of the EDLC cells was explored and the cells were characterised by electrochemical impedance spectroscopy (EIS), cyclic voltammetry and galvanostatic charge–discharge. A generalised equivalent circuit model was developed for which numerical simulations were performed to determine the properties and parameters of its components from the EIS data. It was found that the proposed model fitted successfully the data of all tested cells. PEDOT enhanced the electrode and cell capacitance via its pseudo-capacitance effect up to a maximum value for an optimum PEDOT loading and greatly increased the energy density of the cell while the maximum power density has been still maintained at supercapacitor levels. Furthermore, PEDOT replaced PVDF as a binder and harmful solvent release was reduced during electrode processing. Activated carbon–carbon black composite electrodes with PEDOT as binder were found to have specific capacitance superior to that of activated carbon–carbon black electrodes with PVDF binder.