Solid‐state polymer supercapacitors (SSP‐SCs) have vast potential for future development due to their compact, safe, environment‐friendly, and facile designing. Thus, prevalent researches have been explored in this area. In this article, poly(3,4‐ethylenedioxythiophene) (PEDOT) SSP‐SCs were assembled by using poly(3,4‐ethylenedioxythiophene)/carbon paper (PEDOT/CP) as electrodes and polyvinyl alcohol/sulfuric acid/potassium iodide (PVA/H2SO4/KI) as the gel polymer electrolyte. The effect of KI content on the electrochemical performance of the SC was studied by cyclic voltammetry, galvanostatic charge–discharge measurements (GCD), and electrochemical impedance spectroscopy. The results indicated that the PEDOT SSP‐SC has excellent electrochemical properties when KI doping amount was 60 wt %. The introduction of KI increased the specific capacitance due to the improved ionic conductivity and additional pseudocapacitance reaction at the electrode–electrolyte interface. The PEDOT SSP‐SC showed high energy and power densities of 451.32 Wh kg−1 and 13.29 kW kg−1, respectively, as well as a specific capacitance of 352.59 F g−1 for a discharge current of 1 mA cm−2. In addition, after 1000 GCD cycles, the PVA/H2SO4/KI‐based PEDOT SSP‐SC showed capacitance retention of 74.08%. Therefore, the SC exhibits outstanding energy and power density and good cycle stability and has great potential to be used in high‐energy density equipment. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48723.