To obtain the subject polymer containing an excellent unsaturated group, exhibiting excellent effectiveness as a free radical curing mechanism and useful in the field of protective coating by reacting an anhydride functional polybutylene (derivative) with a specific acryl functional compound.

This functional polymer containing at least one acryl group in the molecule and expressed by the formula I (Z is polybutylene chain; G is a 2-10C alkylene; L is a 1-18C alkyl or H), the formula II, etc., can be produced by reacting (A) an anhydride functional polybutylene (derivative) (e.g. a compound of the formula III) with (B) an acryl functional compound containing at least one OH, Cl, isocyanate group, epoxy group or amine group in addition to acryl group in the molecule (e.g. a compound of the formula HO-G-OC(O)C(L)=CH2, a compound of the formula IV or a compound of the formula V).