Conjugated diene rubber, process for producing the same, and rubber composition

A conjugated diene rubber obtained by a process wherein active conjugated diene polymer chains each having an active metal at a polymer chain terminal, which have been obtained by polymerizing a conjugated diene monomer alone, or a conjugated diene monomer and an aromatic vinyl monomer with the aid of an organic active metal in an inert solvent, are allowed to react with a specific polyorganosiloxane capable of reacting with the active metal bonded to the polymer chain terminal. The conjugated diene rubber contains at least 5% by weight of a structure comprising at least three conjugated diene polymer chains bonded through a polyorganosiloxane. The conjugated diene rubber gives, when silica is incorporated therein, a rubber composition having good processability and giving a crosslinked rubber having reduced heat build-up, good wet grip performance and good abrasion resistance.