A rubber composition containing 100 parts by mass of a rubber component (A) comprising at least one rubber of natural rubber and synthetic diene base rubbers and 5 to 120 parts by mass of a low molecular weight aromatic vinyl compound-diene compound copolymer (B) having a weight average molecular weight (measured by gel permeation chromatography and reduced to polystyrene) of 1,000 to 300,000 and, wherein the copolymer (B) comprises 0 to 80% by mass of an aromatic vinyl compound and has a vinyl bond content of 0 to 80% by mass in the part of the diene compound, and has a cross-linkable functional group at an end. Further, tires produced by using the rubber composition are provided.