PURPOSE: To obtain the titled polymer having high stereo-regularity and excellent heat-resistance, by polymerizing vinylnaphthalene in the presence of a catalyst consisting of trimethylalumium and a titanium halide.

CONSTITUTION: The objective polymer can be produced by polymerizing a vinylnaphthalene (preferably α-vinylnaphthalene) in the presence of a catalyst consisting of a mixture of trimethyl-aluminum and a titanium halide (preferably produced by modifying titanium trichloride with an oxygen-containig compound such as ether, ester, etc., or by supporting titanium tetrachloride on magnesium chloride). The molar ratio of trimethylaluminum to the magnesium halide is preferably 1W100.