A non-aqueous electrolyte solution for a battery, including a compound represented by formula (1), wherein each A represents P or P═O; each R represents H, a halogen, an alkyl, an aryl, an alkoxy or an aryloxy; each X represents H, an alkyl, an aryl, an alkali metal or formula (2); each Y represents H, a halogen, an alkyl, an aryl, an alkoxy, an aryloxy or formula (3); each Z represents H, an alkyl, an aryl or OZ1; Z1 represents H, an alkyl, an aryl, an alkali metal, formula (2), or formula (4); each M represents an alkali metal; n is 1 or more; m is 1 or more; l is 1 or more; a sum of n, m and l in one molecule is from 1 to 200; and each * represents a position of bonding: