A polymer gel electrolyte includes an electrolyte solution composed of a plasticizer with at least two carbonate structures on the molecule and an electrolyte salt, in combination with a matrix polymer. Secondary batteries made with the polymer gel electrolyte can operate at a high capacitance and a high current, have a broad service temperature range and a high level of safety, and are thus particularly well-suited for use in such applications as lithium secondary cells and lithium ion secondary cells. Electrical double-layer capacitors made with the polymer gel electrolyte have a high output voltage, a large output current, a broad service temperature range and excellent safety.