Catalyst olefin polymerization and process for olefin polymerization using the same

A process for olefin polymerization comprising polymerizing an olefin in the presence of a catalyst for olefin polymerization comprising:

• (A) a compound of a transition metal in Group IVB of the Periodic Table, which is represented by the following formula (I'):
• R.sup.1.sub.a R.sup.2.sub.b R.sup.3.sub.c R.sup.4.sub.d M
• wherein M is zirconium;
• R.sup.1 is a ligand having a cyclopentadienyl skeleton;
• R.sup.2, R.sup.3 and R.sup.4 are each a ligand having a cyclopentadienyl skeleton, an alkyl group, a cycloalkyl group, an aryl group, an aralkyl group, an alkoxy group, an aryloxy group, a trialkylsilyl group, SO.sub.3 R (wherein R is a hydrocarbon group of 1 to 8 carbon atoms or a substituted hydrocarbon group of 1 to 8 carbon atoms), a halogen atom or hydrogen atom, a is an integer of not less than 1;
• and a+b+c+d=4, and wherein at least one of R.sup.2, R.sup.3 and R.sup.4 is the ligand having the cyclopentadienyl skeleton;
• (B) an organoaluminum compound;
• and
• (C) a Br.o slashed.nsted acid which is a polystyrene strongly acidic cation-exchange resin having SO.sub.2 OH groups.