The present invention relates to a polymer having a thiol group at one end of the molecule, which is obtained by subjecting the monomers capable of radical polymerization to radical polymerization in the presence of a thiolcarboxylic acid and then treating the resulting polymer with an alkali or acid; to a process for producing the same; and to a block copolymer based on the polymer having a thiol group at the end.The polymer having a thiol group at one end is difficult of forming disulfide linkages by oxidation and thus difficult of becoming insoluble. It is also a highly reactive material that will find wide use in varied application areas. The block copolymer based on the polymer having a thiol group at the end is superior in compatibility and will find wide use in varied application areas.