At present, the polymer matrices of most polymer electrolytes are derived from petroleum-based synthetic polymers. Herein, sustainable and renewable soy protein isolate (SPI) was grafted with methacrylic acid (MAA) and then cross-linked by ring-opening reaction with polyethylene glycol diglycidyl ether as cross-linking agent to obtain a biomass-based polymer electrolyte. Results show that when the added amount of MAA is twice the quality of SPI, gel polymer electrolyte displays the best comprehensive properties and presents the highest ionic conductivity of 5.24 × 10−3 S/cm. The flexible supercapacitor was fabricated by using SPI-based gel polymer electrolyte with activated carbon electrodes, which exhibited excellent specific capacitance (128.63 F/g) and energy density (9.52 Wh/kg) at 0.5 A/g with a decent capacitance retention of 93% after 5000 charge–discharge cycles. It can be ascribed that grafting modification of SPI improves the interface performance of electrode–polymer electrolyte. Furthermore, potassium iodide is introduced to form a redox polymer electrolyte to achieve a high-energy-density supercapacitor, which provides outstanding energy density of 24.40 Wh/kg at 1.0 A/g. This work demonstrates that sustainable and renewable biomass can be converted into matrix of polymer electrolyte for high performance supercapacitor based on aqueous polymer electrolyte.