NOVELTY - A polymer electrolyte comprises an organic electrolyte solution containing a lithium salt dissolved in a non-aqueous solvent.    USE - For rechargeable lithium batteries (claimed).    ADVANTAGE - The invention has good heat-resistance and does not dissolve in an organic electrolyte solution at room or high temperature.    DETAILED DESCRIPTION - A polymer electrolyte comprises:    (1) an organic electrolyte solution with a lithium salt dissolved in a non-aqueous solvent; and    (2) a composite fiber immersed with the organic electrolyte solution.    The composite fiber comprises a gelable fiber which is gelated by the non-aqueous solvent, is cross-linked by a bivalent or multivalent basic cross-linking agent and is gelated by the organic electrolyte solution, and an un gelable fiber which is not gelated by the non-aqueous solvent. The gelable fiber comprises at least two acidic groups and at least two gelable functional groups.    INDEPENDENT CLAIMS are also included for:    (a) A rechargeable lithium battery comprising:    (i) a positive electrode which intercalates and de intercalates lithium ions;    (ii) negative electrode which intercalates and de intercalates lithium ions; and    (iii) polymer electrolyte disposed between the positive and negative electrodes; and    (b) a method of manufacturing a rechargeable lithium battery comprising:    (i) preparing a base polymer by making a composite fiber;    (ii) preparing a gelating liquid by mixing a bivalent or multivalent basic cross-linking agent which cross-links the gelable fiber with an organic electrolyte solution which includes lithium salts dissolved in a non-aqueous solvent;    (iii) inserting into a battery case a positive electrode and a negative electrode that intercalate and de intercalate lithium ions with the base polymer dissolved between the positive and negative electrodes; and    (iv) adding the gelating liquid into the battery case.    DESCRIPTION OF DRAWING(S) - The figure is a schematic diagram showing the cross-linked structure of the polymer electrolyte.