A polymer electrolyte includes an organic electrolyte solution and a composite fiber immersed with the organic electrolyte solution. The organic electrolyte includes lithium salts dissolved in a non-aqueous solvent. The composite fiber includes a fiber that is gelable, and a fiber that is ungelable by the non-aqueous solvent. The gelable fiber has at least two acidic groups and at least two gelable functional groups. The gelable fiber is cross-linked by a bivalent or multivalent basic cross-linking agent, thereby cross-linking the composite fiber.