To obtain an ethylene-vinyl alcohol polymer having excellent workability in the dissolution in water without deteriorating the water-resistance of the coating film and the viscosity stability of the solution.

The objective ethylene-vinyl alcohol copolymer having an ethylene unit content of 2-19 mol% is produced by copolymerizing ethylene and a vinyl ester at 65-150°C under pressurized ethylene atmosphere and saponifying the obtained copolymer.