Abstract: A diene rubber comprised of a conjugated diene homopolymer or a conjugated diene/aromatic vinyl copolymer; the homopolymer or copolymer having on at least one end of its polymer chain a quaternary ammonium group to which four carbon atoms have been bound; at least 10% of the bound conjugated diene units being a vinyl bond; and the homopolymer or copolymer further having a weight average molecular weight (Mw) of 100,000 to 2,000,000. This rubber exhibits well reduced heat build-up, which is an index of a well reduced rolling resistance, and having tensile strength and abrasion resistance.