This invention provides a process by which a polymer having a hydroxyl group at both terminals can be easily obtained with a cheap price and good efficiency from a wide field of vinyl-based monomers including polar ones. The process is arranged in such a manner that the polymerization of a vinyl-based monomer (a) is performed in the presence of an alcohol (b) having no addition-polymerization reactivity by using an initiator (c) consisting essentially of a peroxide and, on this occasion, at least one of catalysts (d) selected from a group consisting of an organic sulfonic acid compound having no addition-polymerization reactivity and an inorganic acid is further used and a reactor does not substantially contain any component other than the (a), (b), (c) and (d).