Although great progress has been made in hydrogel electrolytes for flexible energy storage devices, polyvinyl alcohol (PVA)-based hydrogel electrolytes that combine high self-repairability, stretchability and wide operating temperatures are still a challenge. Here, a novel physically cross-linked self-healing dual-network hydrogel electrolyte (PVA/Agar-EMIMBF₄-Li₂SO₄) is prepared by simple one-pot physical crosslinking and freezing/thawing methods. It was found that the dual-network hydrogel formed after agar addition had better tensile properties than the single-network hydrogel (PVA-EMIMBF₄-Li₂SO₄), and it has excellent flexibility with negligible capacities loss at different bending angles. Interestingly, the dual-network hydrogel electrolyte has excellent temperature tolerant when it contains ionic liquids. Specifically, the dual-network hydrogel electrolyte-based flexible supercapacitor delivers high capacities under a wide operating temperature range of −30 °C to 80 °C. Moreover, the dual-network hydrogel exhibits good self-healing ability, and the healing efficiency can reach more than 80% of the initial state after five self-healing cycles. Our research on PVA-based hydrogel with wide-temperature adaptability, self-repairability and mechanical flexibility presents an encouraging pathway toward other flexible energy storage devices.