To reduce the deposition of scale on the inside wall of a polymerizer by keeping the temperature in the vapor phase at a temperature lower than that of the polymerization solution and thereby controlling a difference between the temperatures in the copolymerization of ethylene with vinyl acetate in the polymerizer.

A polymerizer is charged with 100 pts.wt. vinyl acetate and 0.1-100 pts.wt. solvent being an alcohol having at most 4C, and 0.002-0.2 pt.wt. polymerization initiator being a free radical generator, and an ethylene gas is blown into the polymerizer to produce an ethylene/vinyl acetate copolymer. It is desirable in the copolymerization that the temperature (Ta°C) in the vapor phase and that (Tb°C) in the liquid phase are kept so that they may satisfy the relationship: Ta<Tb, and the temperatures are controlled so that the relationship: (Tb-Ta)≥(Tb/12)2×0.1 may be satisfied. In controlling these temperature conditions, it is desirable that the polymerization is performed while the vapor phase is cooled. An example of the cooling method consists of cooling by means of a cooling jacket provided on the outside of the upper part (vapor phase) of the polymerizer.