Lithium metal polymer battery comprising: - at least one negative electrode comprising a lithium metal or a lithium metal alloy; - at least one positive electrode comprising at least one active material having a potential higher than 3.7V vs Li + /Li, at least one block copolymer P 1 and at least one agent generating electron conductivity, said positive electrode optionally being supported by a current collector; and - at least one solid polymer electrolyte comprising: * at least one block copolymer P 1, or * at least one lithium salt and at least one poly(ethylene oxide) polymer material selected from among a block polystyrene-poly(ethylene oxide) copolymer, a block polystyrene-poly(ethylene oxide)-polystyrene copolymer, a statistical poly(ethylene oxide-stat-propylene oxide) copolymer associated with a reinforcing agent, a statistical poly(ethylene oxide-stat-butylene oxide) copolymer associated with a reinforcing agent, and a poly(ethylene oxide) associated with a reinforcing agent, said reinforcing agent being selected from among cellulose nanofibrils, ceramic nanoparticles and a fluorinated polymer or copolymer, said lithium metal polymer battery being characterized in that: * the active material of the positive electrode is selected from among: active materials of olivine type selected from among those of formula LiT t T' 1-t PO 4 where o < t < 1 and T and T' are different and are selected from among Fe, Mn, Co, Ni and Ti, and those of formula LiMg y Mn 1-y PO 4 where 0 < y ≤ 0.2; active materials of fluorophosphate type; and active materials of LiMO 2 lamellar oxide type where M is a mixture of at least two metals selected from among Al, Ni, Mn and Co; and * the block copolymer P 1 is a diblock copolymer of AB type or triblock of BAB type where block A is a non-substituted polyoxyethylene chain having a number average molecular weight less than or equal to 100 kDa; and block B is an anionic polymer able to be prepared from one or more vinyl monomers substituted by the anion of a lithium sulfonyl (trifluoromethylsulfonyl) imide salt (TFSILi) of following formula: where * is the attachment point of said anion of formula onto said vinyl monomer via a covalent bond of a linear alkyl chain having 1 to 5 carbon atoms or linear alkoxy chain having 1 to 5 carbon atoms. - at least one negative electrode comprising a lithium metal or a lithium metal alloy; - at least one positive electrode comprising at least one active material having a potential higher than 3.7V vs Li + /Li, at least one block copolymer P 1 and at least one agent generating electron conductivity, said positive electrode optionally being supported by a current collector; and - at least one solid polymer electrolyte comprising: * at least one block copolymer P 1, or * at least one lithium salt and at least one poly(ethylene oxide) polymer material selected from among a block polystyrene-poly(ethylene oxide) copolymer, a block polystyrene-poly(ethylene oxide)-polystyrene copolymer, a statistical poly(ethylene oxide-stat-propylene oxide) copolymer associated with a reinforcing agent, a statistical poly(ethylene oxide-stat-butylene oxide) copolymer associated with a reinforcing agent, and a poly(ethylene oxide) associated with a reinforcing agent, * at least one block copolymer P 1, or * at least one lithium salt and at least one poly(ethylene oxide) polymer material selected from among a block polystyrene-poly(ethylene oxide) copolymer, a block polystyrene-poly(ethylene oxide)-polystyrene copolymer, a statistical poly(ethylene oxide-stat-propylene oxide) copolymer associated with a reinforcing agent, a statistical poly(ethylene oxide-stat-butylene oxide) copolymer associated with a reinforcing agent, and a poly(ethylene oxide) associated with a reinforcing agent, * the active material of the positive electrode is selected from among: active materials of olivine type selected from among those of formula LiT t T' 1-t PO 4 where o < t < 1 and T and T' are different and are selected from among Fe, Mn, Co, Ni and Ti, and those of formula LiMg y Mn 1-y PO 4 where 0 < y ≤ 0.2; active materials of fluorophosphate type; and active materials of LiMO 2 lamellar oxide type where M is a mixture of at least two metals selected from among Al, Ni, Mn and Co; and active materials of olivine type selected from among those of formula LiT t T' 1-t PO 4 where o < t < 1 and T and T' are different and are selected from among Fe, Mn, Co, Ni and Ti, and those of formula LiMg y Mn 1-y PO 4 where 0 < y ≤ 0.2; active materials of fluorophosphate type; and active materials of LiMO 2 lamellar oxide type where M is a mixture of at least two metals selected from among Al, Ni, Mn and Co; and * the block copolymer P 1 is a diblock copolymer of AB type or triblock of BAB type where block A is a non-substituted polyoxyethylene chain having a number average molecular weight less than or equal to 100 kDa; and block B is an anionic polymer able to be prepared from one or more vinyl monomers substituted by the anion of a lithium sulfonyl (trifluoromethylsulfonyl) imide salt (TFSILi) of following formula: