Method of producing conjugated diene polymers

A method of producing a conjugated diene polymer which comprises polymerizing at least one conjugated diene compound with a catalyst consisting essentially of the following components (a) to (d):

• Component (a):
• a compound containing a rare earth element of atomic number 57-71 in the Periodic Table or a compound obtained by reacting a compound containing a rare element of atomic number 57-71 with a Lewis base;
• Component (b):
• an aluminoxane;
• Component (c):
• an organoaluminum compound represented by general formula (1):
• AlR1R2R3 (1)
• wherein R1 and R2 are the same or different and are a hydrocarbon group having a carbon number of 1-10 or a hydrogen atom, and R3 is a hydrocarbon group having a carbon number of 1-10 provided that R3 is the same as or different from R1 or R2;
• and
• Component (d):
• a reaction product of a metal halide and a Lewis base.