PURPOSE: To produce in a high yield the title polymer which has a narrow molecular weight distribution and a desired molecular weight, by polymerizing an alkenyl ether in the presence of respectively specified organoaluminum com pound, cation donating compound and ester compound.

CONSTITUTION: An alkenyl ether (A) of formula I (wherein R1 is H or CH3; and R2 is a monovalent organic group) is polymerized in the presence of an organoaluminum compound (B) of formula II (wherein R3 is R2; X is halogen; 0≤m<3, and n≤3, with m+n=3) with the molar ratio of (A) to (B) of 2W1,000, a cation donating compound (C) (e.g., H2O or CH3COOH) with the molar ratio of (A) to (C)≤2, and an ester compound (D) (e.g., ethyl acetate) with the molar ratio of (A) to (D)≥0.1, if desired, in a solvent (E) (e.g., hexane) in an amount 1W100 times by volume as much as the component (A) at 100°C or below to produce a polyalkenyl ether having a degree of polymerization of 2 or above and a molecular weight distribution of 1.3 or below.