PURPOSE: To obtain a catalyst compsn. which consists of a specified zirconium compd. and a catalyst activator consisting of a mixture of an organoaluminum compd. and a dialkylmagnesium and can be used in various solvents and provides olefin polymers.

CONSTITUTION: The objective catalyst compsn. consists of a zirconium compd. (A) of formula I [wherein Cp is a (substd.) cyclopentadienyl; (m) is 1-3; A is a halogen, a 1-6C alkyl or formulas II-IV (wherein R is a 1-10C alkyl, H, a halogen or a metal alkyl); X is a halogen or a 1-6C alkyl; (n) is 0-2; (q) is 0-2 and (p+m+n) is equal to the valence of (z)] and contg. an org. ligand of π- bonding, and a catalyst activator (B) consisting of a mixture of an organoaluminum compd. (i) of formula V (wherein R' is a 1-6C alkyl; (p) is 1 or 2; X' is a halogen; and (k) is the valence of Al) and a dialkylmagnesium compd. (ii) of formulas VI and VII (wherein R" is a 2-8C alkyl; R''' is a 2-8C alkyl being different from R"; (t) is the valence of Magnesium; and (r) is 0.01-1).