A rubber composition comprising the following components:(A) a rubber component comprising at least 50% by weight of a styrene/butadiene copolymer rubber;(B) an azodicarboxylic ester compound represented by the formula ##STR1## wherein X is an alkyl of 3 to 8 carbon atoms, an unsubstituted or substituted phenyl, or an unsubstituted or substituted benzyl;(C) carbon black having a nitrogen absorption specific surface area of 100 to 250 m.sup.2 /g and a dibutyl phthalate absorption number of 110 to 170 ml/100 g;(D) sulfur; and(E) a benzothiazole vulcanization accelerator.This rubber composition shows a high loss factor (tan .delta.) in a low temperature range, and a low loss factor in a high temperature range which when applied to the production of automobile tires, achieves improved braking power on wet, snow covered or frozen road surfaces. Lowered rolling resistance during driving without loss in the strength characteristics of the composition are also exhibited.