A process for producing a polymer hydroxylated at both the terminals thereof from a wide variety of vinylic monomers including polar ones readily and efficiently at a low cost. The process comprises polymerizing a vinylic monomer (a) in the presence of an alcohol (b) which does not enter addition polymerization by using an initiator system (c) essentially comprising a peroxide in such a manner that further use is made of at least one catalyst (d) selected from the group consisting of organic sulfonic acid compounds which do not enter addition polymerization and inorganic acids and that the reactor is substantially free from any component other than the above components (a) through (d).
