PURPOSE: To obtain a polymn. catalyst which is excellent in activity at a high temp. and in activity at a low concn. and facilitates the control of the mol.wt. of the resulting polymer by compounding an organometallic compd. of a group IIIA metal, a Lewis base, and an organoaluminum compd. as the main components.

CONSTITUTION: A polymn. catalyst mainly comprises an organometallic compd. of a group IIIA metal, a Lewis base, and an organoaluminum compd. An example of the organometallic compd. of a group IIIA metal is a compd. of the formula (wherein Cp' is a cyclopentadienyl group or an optionally substd. cyclopentadienyl group, and two Cp's may be crosslinked and may be the same or different; M is a transition metal of the group IIIA; R is H, a halogen, a 1-20C hydrocarbon group, a 1-20C oxygen- or silicon-contg. group; A is an org. aluminum compd. or a Lewis base; and n is 0, 1-3 provided that when n is 2 or 3, all the As may be the same or different from each other).