A solid polymer electrolyte for a battery is disclosed. The solid polymer electrolyte includes solid polymer electrolyte including a diblock copolymer AB or a triblock copolymer of the BAB type, in which block A is an unsubstituted polyethylene oxide chain having a number-average molecular weight less than 80,000 g/mol; block B is an anionic polymer prepared from one or more monomers selected from vinyl monomers and derivatives thereof to which is grafted an anion of lithium salt, and a second monomer having cross-linking functions.