It is to provide a method for producing a polymer by a living anionic polymerization, wherein the number of functional groups and the introduction position are accurately specified in the polymer. For this purpose, a cinnamyl alcohol represented by the following formula [I] or a derivative thereof is subjected to a reaction when conducting a living anionic polymerization. In formula [I], R1 represents an alkyl group or alkoxy group; m represents an integer of 0 to 5 and when m is 2 or more, R1s may be the same or different; R5 represents a hydrogen atom, alkali metal atom, trialkylsilyl group or a substituent represented by the following formula [II]. In formula [II], R3 represents a hydrogen atom or a C1-C6 alkyl group; and R4 represents an alkyl group which may be substituted by an alkoxy group, a cycloalkyl group which may be substituted by an alkoxy group, a phenyl group which may be substituted by an alkyl group, or a phenyl group which may be substituted by an alkoxy group).