In this work, solid-state polymer supercapacitor (SSC) was assembled using poly(3,4-ethylenedioxythiophene/carbon paper (PEDOT/CP) as an electrode and ionic liquid (1-butyl-3-methylimidazole tetrafluoroborate)/polyvinyl alcohol/sulfuric acid (IL/PVA/H₂SO₄) as a gel polymer electrolyte (GPE). The GPE was treated through freezing–thawing (F/T) cycles to improve the electrochemical properties of PEDOT SSC. Cyclic voltammetry (CV), galvanostatic charge–discharge measurements (GCD) and electrochemical impedance spectroscopy (EIS) techniques and conductivity were carried out to study the electrochemical performance. The results showed that the SSC based on ionic liquid GPE (SSC-IL/PVA/H₂SO₄) has a higher specific capacitance (with the value of 86.81 F/g at 1 mA/cm²) than the SSC-PVA/H₂SO₄.The number of F/T cycles has a great effect on the electrochemical performance of the device. The energy density of the SSC treated with 3 F/T cycles was significantly improved, reaching 176.90 Wh/kg. Compared with the traditional electrolytes, IL GPE has the advantages of high ionic conductivity, less volatility, non-flammability and wider potential window. Moreover, the IL GPE has excellent elastic recovery and self-healing performance, leading to its great potential applications in flexible or smart energy storage equipment.