To introduce an alcoholic hydroxyl group into the terminal of a hydrocarbon-based polymer prepared by a cationic polymerization without using a special and expensive raw material such as a hydrido-borane reagent by reacting a specific hydrocarbon-based polymer with a specified compound.

(A) A hydrocarbon-based polymer having a phenolic hydroxyl group at the terminal is reacted with (B) a compound reactive with the phenolic hydroxyl group and capable of producing an alcoholic hydroxyl group to produce the objective polymer having a group represented by the formula [R1 is a 1-20C bivalent organic group; R2 and R3 are each H or a 1-10C monovalent organic group; R4 is a 1-10C monovalent organic group; (n) is 0-4] at the terminal. The component A is preferably prepared by a Friedel-Crafts type reaction of (A) a hydrocarbon-based polymer obtained by a cationic polymerization and having a halogen atom at the terminal with (B) phenols.