Dipalladium complex with a macrocyclic ligand having two diimine sites catalyzes copolymerization of ethylene with acrylic anhydride to afford the copolymer containing the repeating unit from acrylic anhydride. The obtained copolymer contains the cyclic and acyclic anhydride groups in high content (up to 5.7 mol %) in the main chain. It is contrasted with that the monopalladium complex with the diimine ligand catalyzes the reaction to yield the copolymer having the polar group at the end of branches with lower content (0.8 mol %). Decreased ethylene pressure of the reaction using the dipalladium catalyst results in increase in the polar comonomer unit content. Methanolysis of the copolymer takes place smoothly to give the polymer with both carboxylic acid and ester groups in the polymer chain.