PURPOSE: To produce a highly syndiotactic styrenic polymer efficiently at a low cost by adding a specific chain transfer agent to a catalyst system comprising a transition metal compd., a coordination compd., and an alkylating agent in the process for polymerizing a styrenic monomer using the catalyst system.

CONSTITUTION: A catalyst system comprising a transition metal compd., a compd. capable of reacting with the foregoing compd. to form an ionic complex or an oxygen-contg. compd. of formula I and/or formula II (wherein R1 to R7 are each 1-8C alkyl; Y1 to Y5 are each an element of the group 13; and a, b, c, and d are each 0-50 provided a+b and c+d are each 1 or higher), and an alkylating agent (e.g. triethylaluminum) is prepd. in advance. A reaction product of an alkylaluminum having linear alkyl groups each having at least two carbon atoms (e.g. tri-n-butylaluminum) with water is added as a chain transfer agent to the catalyst system, which is then used to polymerize a styrenic monomer to give a highly syndiotactic styrenic polymer.