A rubber composition suitable for tire treads having well-balanced excellent wet skid characteristic, ice skid characteristic and rolling characteristic, and an excellent processability, which comprises a rubber component containing at least 20 % by weight of 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 at most 5 % by weight and a content of 1,2-bonds in the conjugated diene component of at least 10 % by weight,
(B) the block B having a content of an aromatic vinyl compound of 25 to 50 % by weight and a content of 1,2-bonds in the conjugated diene component of at least 10 % by weight,
(C) a content of the block A in the block copolymer being from 20 to 80 % by weight,
(D) a content of the aromatic vinyl compound in the block copolymer being from 5 to 30 % by weight and a 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 dicarboxylic acid diester.