A series of sulfonated poly(fluorenyl ether nitrile oxynaphthalate) (SPFENO) copolymers with different degrees of sulfonation were synthesized. Their degree of sulfonation was controlled by adjusting the molar ratio of the reactants. The polymer electrolytes prepared with a SPFENO membrane exhibited high ionic conductivities and solution holding capacity, which depended on the degree of sulfonation. The quasi-solid-state electric double layer capacitors (EDLCs) consisted of activated carbon electrodes and polymer electrolytes were assembled, and their electrochemical characteristics were studied by cyclic voltammetry and charge-discharge cycle tests. A SPFENO membrane with proper degree of sulfonation was effective for maintaining high ionic conductivity and keeping good electrode–electrolyte interfacial contact during cycling, which resulted in good cycling performance of the EDLC.