The invention provides a battery separator comprising a porous resin film and a crosslinked polymer supported thereon and having iminodiacetic acid groups in side chains of the polymer chains. The iminodiacetic acid group is preferably represented by the formula wherein M1 and M2 are each independently a hydrogen atom, a lithium atom, a potassium atom, a sodium atom, or triethylamine. It is preferred that the layer of the crosslinked polymer is substantially nonporous or solid, and ion conductive, and that the crosslinked polymer has in the molecule oxetanyl groups which are capable of cation polymerization.