Quasi-solid-state supercapacitors were assembled using a pair of activated carbon electrodes and two polyvinyl alcohol (PVA)-H2SO4 gel polymer electrolytes (GPEs) containing respectively redox additives of hydroquinone (HQ) and methylene blue (MB), which were separated by a Nafion 117 membrane in a sandwich-type configuration. PVA-H2SO4-HQ and PVA-H2SO4-MB GPEs worked on the sides of the positive and negative electrodes of the supercapacitor, respectively. The electrochemical performances of the supercapacitor with optimized PVA-H2SO4-HQ and PVA-H2SO4-MB GPEs were evaluated by cyclic voltammetry, galvanostatic charge-discharge and electrochemical impedance spectroscopy techniques. After the introduction of HQ and MB, the supercapacitor with PVA-H2SO4-HQ|PVA-H2SO4-MB GPEs can exhibit high specific capacitance of 563.7Fg−1 and energy density of 18.7WhKg−1, increasing by about fourfold in comparison with a supercapacitor with a PVA-H2SO4 GPE. The improved energy storage is ascribed to the reversible Faradaic reactions related to HQ and MB in the corresponding gel polymer electrolytes. Additionally, the supercapacitor shows excellent cyclic durability with 90.0% capacitance retention after 3000 cycles.