Polymers having an oxetanyl group on the side chain and being represented by the following formula (2) are provided. They are usable for reactions such as ring-opening reaction and addition reaction. The process comprises subjecting to anionic ring-opening polymerization a 3-[(oxiranylmethoxy)methyl]oxetane monomer represented by the following formula (1) alone or together with other monomer containing an epoxy group: wherein A represents a hydrogen atom or an alkyl group of 1-6 carbon atoms, wherein A is the same as above, and R represents a hydrogen atom, a chloromethyl group, straight chain alkyl group or branched chain alkylene group of 1-12 carbon atoms, phenyl group, straight or branched chain alkyloxymethyl group of 1-12 carbon atoms or phenoxymethyl group, and n and m each represent a molar fraction, n being 100-1 mol %, m being 0-99 mol % with n+m=100.