The low energy density of supercapacitors, especially supercapacitors based on aqueous electrolytes, is the main factor limiting their application, and the energy density is closely related to the operating potential window of the supercapacitor. The polymer electrolyte is the main contributor to the safe operation and good ion conductivity of the supercapacitor. In this study, a crosslinked quaternized poly(arylene ether sulfone) (PAES) membrane was prepared via crosslinking during membrane formation with a thermal‐only treatment and applied in an electric double‐layer capacitor (EDLC). The pre‐prepared PAES membrane formed a polymer electrolyte with 1 mol/L Li2SO4 and was then fabricated into an EDLC single cell. The properties of both the membrane and ELDC were investigated. The preferred cPAES‐N‐0.2 polymer electrolyte showed an ionic conductivity of 1.18 mS/cm. The optimized EDLC exhibited a single‐electrode gravimetric capacitance of 104.92 F/g at a current density of 1.0 A/g and a high operating potential window (1.5 V); it, thereby, achieved a high energy density of 8.20 W h/kg. The EDLC also exhibited excellent cycling properties over 3000 charge–discharge cycles. The crosslinked structures promoted the tensile strength and thermal stability of the PAES membranes; this was accompanied by a slight decrease in the ionic conductivity. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47759.