PURPOSE: To provide the titled polymer composed of a specific structural unit, having a specific functional group such as carboxyl group on side chain and giving a pervaporation membrane effective especially in separating water from a mixture of water and a polar organic material.

CONSTITUTION: The objective α-fluoroacrylic acid polymer composed of 5W100% structural unit of formula I [X1 is carboxyl which may be substituted with alkali metal, etc., CONR4R5 (R4 is H, 1W20C alkyl; R5 is H, 1W20C hydroxylkyl, etc.), etc.], 0W95% structural unit of formula II (X2 is H, F or methyl; X3 is 1W10C alkyl, 2W10C fluoroalkyl, etc.) and 0W95% structural unit of formula III. The polymer wherein X1 is carboxyl can be produced by (co)polymerizing the monomer of formula IV and, if necessary monomer of formula V and/or formula VI and optionally hydrolyzing the side chain originated from vinyl acetate of formula VI. The polymer can be crosslinked with e.g. ethylenediamine to increase the membrane strength.