PURPOSE: The titled polymer excellent in heat resistance, adherence and adhesiveness prepared by graft-polymerizing an unsaturated carboxylic acid onto a linear 4-methyl-1-pentene polymer and then attaching a halogen atom.

CONSTITUTION: The titled substantially linear polymer wherein saturated carboxylic acid (anhydride) component units (B) are graft-polymerized onto the linear trunk polymer (A) comprising 55W100wt% 4-methyl-1-pentene component units and 45W0wt% other 2W20C α-olefin component units, halogen atoms are bonded, the rate of grafting of component B is 0.05W20wt%, based on the total polymer produced, the content of c atoms is 5W75wt%, based thereon, and the intrinsic viscosity η as measured in a decalin solvent at 135°C is 0.05W5. This is useful as a coating composition for clean coat, paints, lacquers, inks, etc., in the form of a solution or aqueous dispersion composition.