Hydrogel polymer electrolytes (GPEs), as an important component of flexible energy storage devices, have gradually received wide attention compared with traditional liquid electrolytes due to their advantages of good mechanical, bending, and safety properties. In this paper, two cross-linked GPEs of poly(acrylic acid-co-acrylamide) or poly(acrylic acid-co-N-methylolacrylamide) with NaNO3 aqueous solution (P(AA-co-AM)/NaNO3 or P(AA-co-HAM)/NaNO3) were successfully prepared using radical polymerization, respectively, using acrylic acid (AA) as the monomer, N-methylolacrylamide (HAM) or acrylamide (AM) as the comonomer, and N, N-methylenebisacrylamide (MBAA) as the cross-linking agent. We investigated the morphology, glass transition temperature (Tg), ionic conductivities, mechanical properties, and thermal stabilities of the two GPEs. By comparison, P(AA-co-HAM)/NaNO3 GPE exhibits a higher ionic conductivity of 2.00 × 10−2 S/cm, lower Tg of 152 °C, and appropriate mechanical properties, which are attributed to the hydrogen bonding between the -COOH and -OH, and moderate cross-linking. The flexible symmetrical supercapacitors were assembled with the two GPEs and two identical activated carbon electrodes, respectively. The results show that the flexible supercapacitor with P(AA-co-HAM)/NaNO3 GPE shows good electrochemical performance with a specific capacitance of 63.9 F g−1 at a current density of 0.2 A g−1 and a capacitance retention of 89.4% after 3000 charge–discharge cycles. Our results provide a simple and practical design strategy of GPEs for flexible supercapacitors with wide application prospects.