A rubber composition suitable for tire treads having well-balanced excellent steering stability in cornering, wet skid characteristic, ice skid characteristic and rolling characteristic, and an excellent processability, which comprises a rubber component containing a block copolymer consisting essentially of a block A and a block B, obtained by conducting polymerization of an aromatic vinyl compound and a conjugated diene compound in a hydrocarbon solvent in the presence of an organolithium initiator and modifying with a coupling agent, and satisfying the following conditions (A) to (E);
(A) the block A having a content of an aromatic vinyl compound of 5 to 20 % by weight and a content of 1,2-bonds in the conjugated diene component of 25 to 55 % by weight, (B) the block B having a content of an aromatic vinyl compound of 35 to 60 % by weight and a content of 1,2-bonds in the conjugated diene component of 20 to 70 % by weight, (C) the content of the block A in the block copolymer being from 20 to 80 % by weight, (D) the average content of the aromatic vinyl compound in the block copolymer being from 20 to 40 % by weight and the average content of 1,2-bonds in the conjugated diene component of the block copolymer being from 20 to 60 % by weight, and (E) at least 40 % by weight of the polymer chains of the block copolymer being a branched polymer formed by modification with a trifunctional or tetrafunctional coupling agent.