Conjugated diene polymer and rubber composition

A rubber composition comprising 10-200 parts by weight of silica based on 100 parts by weight of a rubber ingredient consisting of 10-100% by weight of a conjugated diene polymer having a content of cis-1,4-bond of not less than 85%, a content of 1,2-vinyl bond of not more than 2.0% and ratio of weight average molecular weight (Mw) to number average molecular weight (Mn) of not more than 5, wherein the conjugated diene polymer contains at least one functional group selected from the group consisting of an epoxy group and a hydroxyl group in its molecule and 90-0% by weight of another diene polymer or natural rubber, wherein said conjugated diene polymer is obtained by polymerizing a conjugated diene compound with a catalyst consisting essentially of the following components (a) to (c) and subsequently reacting with at least one compound selected from the group consisting of the following components (d) and (e):

• Component (a):
• a compound containing a rare earth element belonging to atomic numbers 57-71 in the Periodic Table excepting a halogen-containing compound, or a reaction product between such a compound and a Lewis base;
• Component (b):
• an aluminoxane and an organoaluminum compound having a general formula of AlR1R2R3 (wherein R1 and R2 are the same or different and are a hydrogen atom and a hydrocarbon group having a carbon number of 1-10, and R3 is a hydrocarbon group having a carbon number of 1-10, provided that R3 is the same as or different from R1 and R2);
• Component (c):
• a halogen-containing compound;
• Component (d):
• a hydroxyl group-containing vinyl compound;
• Component (e):
• an epoxy compound.