Disclosed herein is a rubber composition comprising at least 20% by weight of styrene-butadiene copolymer based on the total weight of the rubber content. The styrene-butadiene copolymer is obtained by randomly copolymerizing styrene with 1,3-butadiene in a hydrocarbon solvent in the presence of an organolithium compound as an initiator and then subjecting to a coupling reaction with a polyfunctional coupling agent, and contains 30-70% by weight of branched polymers therein, and has the following properties:(a) a content of bound styrene in the copolymer 3-15% by weight;(b) a content of vinyl bonds contained in the butadiene units is 15-30% by weight;(c) a Mooney viscosity (ML.sub.1+4.sup.100.degree. C.) is 15-50; and(d) a molecular weight distribution of the copolymer is bimodal at a ratio Mw/Mn of 1.4-2.2 in which Mw is a weight-average molecular weight and Mn is a number-average molecular weight.