Solid-state electrolytes such a further novel finding is going to have great importance because of the disadvantages of liquid electrolytes such as electrochemical instability, low ion selectivity, and interface contact. It is anticipated that the use of solid-state electrolytes including supercapacitors (SCs) will become widespread with decreasing self-leakage and environmental damage more than liquid electrolytes. In this study, SCs with graphene/PEDOT: PSS coated electrodes and binary PVA gel electrolytes with a conductive layer were designed and the electrochemical performance of the configurations was characterized. The effects of the conductive layer between binary electrolytes and the concentration of the KOH solution in the electrolytes were studied. It was observed that the conductive layer used between the gel electrolytes causes additional charging at the electrolyte/conductive layer interface and behaves like a serially connected capacitor to the double-layer capacitor. Interestingly, at a slow sweep rate (5 mV/s), the specific capacitance values of the assembled SCs decreased when a conductive layer was used but it increased when the sweep rate was fast (100 mV/s).