Flexible supercapacitors have attracted increasing interest due to their high power density, long-term cycling life and excellent safety. Like other energy storage devices, flexible supercapacitors exhibit serious performance degradation as they work in extremely cold and/or sweltering climates, which greatly limit their practical applications. Here, we demonstrate a polymer hydrogel with high ionic conductivity for flexible supercapacitors with high performance and excellent climate tolerance. The wide temperature adaptability of the polymer hydrogel is enabled by introducing an additive of dimethyl sulfoxide, which can form abundant hydrogen bonds with water molecules and functional groups of polymer molecules. The optimized hydrogel exhibits high ionic conductivities of 0.82 and 1.12 S m⁻¹ at −20 and 100 °C, respectively, comparable with that at room temperature. Using the polymer hydrogel as an electrolyte, the resulting supercapacitors not only show high electrochemical performance, but also exhibit high capacitance retention up to 91% and 85% at both low (−20 °C) and high (100 °C) temperatures, compared with that at room temperature. In addition, the developed supercapacitors possess excellent mechanical flexibility even at −20 °C. Polymer hydrogels with wide temperature tolerance could be easily functionalized and broadly used for other flexible energy devices and electronics working in harsh environments in the future.