PURPOSE: To produce a highly syndiotactic styrenic polymer at a high productivity by continuously supplying to a horizontal self-cleaning reactor a styrene monomer and a catalyst both divided into several portions along the axial direction of the reactor and polymerizing the monomer.

CONSTITUTION: A horizontal self-cleaning twin-screw reactor is partitioned into several parts along the axial direction, and these parts (F1, F2, F3, etc.) are each equipped with a jacket (J1, J2, J3, etc.) through which cooling water passes, monomer nozzles (M1, M2, M3, etc.) which supply a styrenic monomer, catalyst nozzles (C1, C2, C3, etc.) which supply a catalyst, and temp. measurement means (T1, T2, T3, etc.). Thus, the catalyst alone or together with the monomer is divided along the axial direction of the reactor and continuously supplied to the reactor where the monomer is polymerized, thus continuously producing a highly syndiotactic styrenic polymer. Examples of the catalyst are methylaluminoxane and triisobutylaluminum.