A fluorine-containing graft copolymer is made from a backbone of an olefin polymer material to which is graft polymerized (a) at least one gaseous fluorinated monomer such as vinylidene fluoride, (b) at least one fluorinated acrylic acid or ester, (c) a mixture of (a) and (b), or (d) a mixture of (a) and/or (b) and a non-fluorinated monomer such as methyl methacrylate. An organic peroxide or a polymeric peroxide is used as the initiator for the graft polymerization process. The graft copolymers have improved surface properties and oxygen barrier properties, and improved thermal stability.