Abstract: A method for preparing an .alpha.-olefin polymer in which an .alpha.-olefin is polymerized in the presence of a catalyst, characterized in that the catalyst is a solid obtained by making the following components (ii) and (iii) be supported in the component (i):Component (i): an organic porous polymer having an average particle diameter of 5 to 1,000 .mu.m, in which the total pore volume of all pores whose diameter is 0.006 to 10 .mu.m is 0.3 cc/g or more, and the total pore volume of all pores whose diameter is 0.05 to 2 .mu.m is 50% or more of the total pore volume of all pores whose diameter is 0.006 to 10 .mu.m;Component (ii) a compound having the structure ##STR1## in which R is a hydrocarbon group having 1 to 10 carbon atoms; and Component (iii) a compound of a transition metal which belongs to one of the Groups IVB to VIB in the Periodic Table, having at least one conjugated 5-membered cyclic ligand.