PURPOSE: To obtain a stereoregular vinyl aromatic polymer having a syndiotactcity of 50% or more and useful for the production of a molded product that is less deformed by temperature by polymerizing a vinyl aromatic monomer using a specified metal complex catalyst.

CONSTITUTION: A vinyl aromatic monomer, such as styrene, is brought in contact with a metal complex catalyst represented by the formula [CpmMXnX'p]+A- at 0 to 160°C with the molar ratio of the monomer to the catalyst being (100:1) to (500,00:1) to obtain a vinyl aromatic polymer having syndiotactcity of 50% or more and preferably 70% or more. In the formula Cp represents η5- cyclopentadienyl or η5-substituted cyclopentadienyl, M represents a metal of Group III, IV, V, VI, VIII, IV or X, or the Lanthanide Series (e.g. Ti or Zr), X represents an inactive anion ligand (e.g. H, a hydrocarbon group or a silyl group), X' represents an inactive neutral donating ligand, m and p are each 0 or 1, n is 1 or more, and A- represents a noncoordinating amphoteric anion of a Brnsted acid salt (e.g. tetrakis-pentafluorophenyl borate).