PURPOSE: To obtain a styrene-butadiene copolymer of improved resilience and heat build-up resistance, by copolymerizing styrene with butadiene in the presence of a Lewis base under a specified condition and adding a polyfunctional coupling agent to the product.

CONSTITUTION: The purpose copolymer is obtained by adding a Lewis base to a polymerization system in which styrene is copolymerized with butadiene in a hydrocarbon solvent by using an organolithium compound as a polymerization initiator; initiating the copolymerization of the styrene with a portion of the butadiene to be added; continuously or intermittently adding the remaining portion of the butadiene to be added, in such a way that the styrene monomer content of the monomer component in the polymerization system is always maintained at a value which is at most twice the bound styrene content of the copolymer finally produced till the conversion to the polymer reaches 98wt%; and adding a polyfunctional coupling agent after completion of the copolymerization.