Flexible supercapacitors have great potential applications in wearable and portable electronics, but their practical applications were limited due to the low energy density and mechanical flexibility of solid-state electrolytes used for the construction of flexible supercapacitors. In this study, we first report the solid-state double-network (DN) hydrogel electrolytes (HEs) incorporated with Na2MoO4 redox additives. It is found that the solid-state DN HEs with Na2MoO4 redox additives exhibit high electrochemical performance, excellent mechanical properties, and fast self-recovery features. We then demonstrate novel symmetric supercapacitors (SSCs) incorporated with the solid-state Na2MoO4 DN HEs and the active carbon cloths as the electrodes. The SSCs exhibit a specific capacitance of 84 mF/cm2 at a current density of 1 mA/cm2 and an energy density of 70 μWh/cm2 at a power density of 3800 μWh/cm2. Moreover, the SSCs retain approximately 80% capacitance retention after 7000 charge/discharge cycles, which indicates that the SSCs possess excellent flexibility and stability. All of these results demonstrate that the SSCs incorporated with the solid-state Na2MoO4 DN HEs as energy-storage devices have great practical applications in wearable and portable electronics.