PURPOSE: To obtain the title copolymer excellent in oxygen barrier property, by polymerizing ethylene with vinyl acetate in the presence of a specified catalyst in an aqueous PVA solution.

CONSTITUTION: An aqueous solution (a) is obtained by dissolving 5W25wt% PVA with a degree of saponification of 80W99% and degree of polymerization of 100W2,000, obtained by saponifying polyvinyl acetate in water. Ethylene (b) at an ethylene pressure of 10W100kg/cm2, vinyl acetate (c) at a weight ratio of component (b) to component (c) of 5W50/95W50 and, optionally, 60wt% or below acrylonitrile-based monomer (d) are polymerized together at 0W100°C, preferably 40W60°C for 2W6hr in the presence of a tetravalent cerium compound (e) (e.g., ceric ammonium intrate) as a catalyst in component (a) containing 10W60wt%, based on the polymer to be produced, PVA until the residual monomer content decreases to 1% or below.