PURPOSE: To produce a polyolefin excellent in physical properties and processibility at a high catalytic activity by using the catalyst obtd. by combining a metallocene compd., an organoaluminum compd., and a metal salt of boric acid.

CONSTITUTION: The catalyst is prepd. by combining a metallocene compd. of formula I (wherein Cp1 and Cp2 are each independently a (substd.) cyclo- pentadienyl group; R1 is a 1-4C alkylene, dialkylsilicon, dialkylgermanium, or alkylamino group; m is 0 or 1; M is Ti, Zr, or Hf; and R2 and R3 are each H, a 1-12C hydrocarbon group, etc.). an organoaluminum compd. of formula II (wherein R4 is H, alkyl. etc.), and a metal salt of boric acid of formula III (wherein C is an alkali or alkaline earth metal cation; L is a Lewis base; A is an anion contg. a boron atom; n is 0-6; and b and d are each such an integer that electric charges of the cation and anion are in balance).