PURPOSE: To produce a butylene polymer continuously in good efficiency, by polymerizing a butane-butylene fraction in the presence of a Friedel-Crafts catalyst and washing the polymer successively with deionized water, a sodium hydroxide solution, and deionized water.

CONSTITUTION: A butane-butylene fraction obtained by extracting butadiene from a C4 fraction obtained from the thermal cracking of naphtha or the like is polymerized in the presence of a Friedel-Crafts catalyst. The obtained butylene polymer is then subjected to washing treatment. Namely, the polymer is wahsed first with deionized water. The polymer from which acids are thus removed by the washing is then washed with a sodium hydroxide solution. The polymer thus washed is withdrawn from the top of an alkali washing tank and further washed with deionized water.