A catalyst for polymerization of olefin is provided which comprises (A) a metallocene compound, (B) an organoaluminum compound, and (C) a metal borate or a metal aluminate. The metallocene compound (A) is represented by the general formula (1) below: ##STR1## where Cp.sup.1 and Cp.sup.2 are cyclopentadienyl group; R.sup.1 is an alkylene, arylalkylene, dialkylsilylene, dialkylgermanylene, alkylphosphinediyl, or alkylimino group, R.sup.1 crosslinking Cp.sup.1 and Cp.sup.2 together; m is 0 or 1; M is titanium, zirconium, or hafnium; and R.sup.2 and R.sup.3 are independently hydrogen, halogen, or a hydrocarbon group, an alkoxy group, or an aryloxy group having 1 to 12 carbons, the organic aluminum compound (B) is represented by the general formula (2) below:AlR.sup.4.sub.3 (2)where each R.sup.4 is independently hydrogen, alkyl, alkoxy, or an aryl group, at least one R.sup.4 being an alkyl group, and the metal borate or the metal aluminate (C) being represented by the general formula (3):(C(L).sub.n).sub.b (A).sub.d (3)where C is an alkali metal cation or an alkaline earth metal cation; L is a Lewis base; A is an art ion having elemental boron or elemental aluminum; n is an integer of from 0 to 6; b and d are respectively an integer selected to balance the electric charge.