An apparatus for continuous polymerization with a simple constitution to produce a polymer having a high quality, as well as a method for producing the polymer using the apparatus, are provided. The apparatus comprises a vessel; a means for supplying a monomer to the vessel; a means for supplying a polymerization initiator to the vessel; a means for detecting a temperature in the vessel; a means for regulating a temperature of an outer wall surface of the vessel so as to have a preset temperature; and a means for controlling a supply flow rate of the monomer and/or the polymerization initiator to the vessel by the monomer supply means and/or the initiator supply means so that the temperature in the vessel becomes substantially the same temperature as the preset temperature.