To improve the cycle durability of a battery by setting copolymer containing monomer unit composed of vinylidene fluoride and α-fluoroacrylate to a matrix of electrolyte and providing polymer electrolyte containing solution composed of solute of lithium salt and solvent solving the lithium salt.

α-fluoroacrylate of monomer unit is expressed by the formula. In the formula, R is CH2(CF2)nH, CH2(CF2)nF, (CH2)nH, (CF2)nF; n=1-6. The weight ratio of vinylidene fluoride to α-fluoroacrylate is preferably 1/99-99/1 and the molecular weight is desirably to be 10,000-200,000. Carbonate is optimal for the solvent of the lithium salt solution and propylene carbonate and ethylene carbonate are adaptable. This lithium battery using fluorine-containing electrolyte is superior in stability of polymer electrolyte, has superior electric conductivity, and superior in the cycle durability because of its superior bond between the electrolyte and electrode material.