An ethylene-vinyl alcohol copolymer (EVOH) solution is introduced into a tower vessel (1) from a first inlet (2) provided at an upper portion of the tower vessel (1). Water vapor is introduced into the tower vessel (1) from a second inlet (3) provided at a lower portion of the vessel (1). The EVOH solution moves downward in the vessel (1), while the water vapor moves upward. The EVOH solution is kept in counter-flow contact with the water vapor. Water is supplied from a water supplying portion (5) located between the first inlet (2) and a tower top (4), whereby a water layer is formed above the first inlet (2). A water/methanol vapor mixture is extracted from the tower top (4) and condensed in a condenser (6) to be thereby recovered in the form of a methanol aqueous solution. Droplets of the EVOH solution contained in the water/methanol vapor mixture are trapped in the water layer formed above the first inlet (2) and, therefore, are less liable to be introduced into the condenser (6). This suppresses extraction of the droplets of the EVOH solution together with the vapor to the outside of the tower vessel (1) during replacement of the EVOH solution with water in the tower vessel (1).