PURPOSE: To obtain the aimed polymer having excellent adhesiveness to glass and polar resins and low melt flow rate, by bringing an unsaturated carboxylic acid and an olefin into contact with a granular olefin polymer and carrying out graft polymerization by using a specific radical initiator.

CONSTITUTION: (B) An unsaturated carboxylic acid or a derivative thereof and (C) an olefin are brought into contact with (A) a granular olefin in an inert gas substantially in the absence of a liquid medium and graft copolymerization is carried out by using (D) a radical initiator at a temperature lower than the melting temperature of the component A to give the aimed polymer. The component B is preferably selected from a group consisting of compounds shown by formula I and formula II (R1 and R2 are H or aliphatic polymer; R3 is H, aliphatic hydrocarbon or aromatic hydrocarbon), the component C has preferably 2W5 carbons and the component A is preferably a homopropylene polymer or a copolymer of propylene and an olefin except propylene.