NOVELTY - A solid electrolyte (S1) provided between a cathode and an anode comprises a multi-layer structure having at least three layers. A layer nearest to the cathode side and a layer nearest to the anode side of the layers include first polymer. At least one layer except the layers located at positions nearest to the cathode and the anode sides of the layers includes a second polymer.    USE - In lithium-ion battery (claimed).    ADVANTAGE - The solid electrolyte provides improved utilization factor of cathode and anode; is excellent in its battery characteristics, lithium-ion battery. The solid electrolyte provides good adhesion to a cathode and an anode and high ionic conductivity.    DETAILED DESCRIPTION - A solid electrolyte (S1) provided between a cathode and an anode comprises a multi-layer structure having at least three layers. A layer nearest to the cathode side and a layer nearest to the anode side of the layers include first polymer. At least one layer except the layers located at positions nearest to the cathode side and the anode side of the layers includes a second polymer that has a functional group capable of being cross-linked and is cross-linked. The first polymer has a low glass transition point, do not have functional groups capable of being cross-linked and not cross-linked. INDEPENDENT CLAIMS are included for the following:    (1) a solid electrolyte (S2) provided between a cathode and an anode comprises parts including polymers high in their cross-linking density in parallel with the electrode planes of the cathode and the anode. The cross-linking density is inclined so as to be lowered toward the cathode and the anode from the part high in its cross-linking density;    (2) a lithium-ion battery having a cathode and an anode capable of being doped with and dedoped from lithium and (S1) or (S2) provided between the cathode and the anode; and    (3) production of the lithium-ion battery involving: forming on the cathode and the anode first polymer layers having a low glass transition point and no functional group capable of being cross-linked and including a polymer which is not cross-linked; forming a second polymer layer provided between the cathode and the anode so as to be opposed to the first polymer layer, having a functional group capable of being cross-linked and including a cross-linked polymer; and allowing the first polymer layer respectively formed on the cathode and the anode and the second polymer layer to be opposed to each other and come into tightly contact with each other.