The present invention provides a rubber composition, in which abrasion resistance and gripping performance are improved in a balanced manner and bleeding of the components is inhibited, and a tire using the composition. Specifically, the present invention provides a rubber composition comprising (B) 10 to 200 parts by weight of a low molecular weight aromatic vinyl-conjugated diene copolymer having weight average molecular weight of 1.0.times.10.sup.3 to 1.0.times.10.sup.5 and aromatic vinyl content of 10 to 75% by weight, wherein the hydrogenation ratio of double bonds in the conjugated diene part is 20 to 60%, based on (A) 100 parts by weight of a rubber component containing at least 60% by weight of a styrene-butadiene copolymer having weight average molecular weight of 5.0.times.10.sup.5 to 2.5.times.10.sup.6 and styrene content of 20 to 60% by weight, wherein the amount of vinyl bonds in the butadiene part is 20 to 70%; which satisfies the following equation 5% by weight