Rubber composition

A rubber composition (COM) obtained by dissolving solution polymerized polybutadiene rubber or solution polymerized styrene-butadiene copolymer rubber having a glass transition temperature (Tg) of −100° C. to −40° C. in an organic solvent to form a starting rubber solution, then by adding and mixing thereto silica or mixture of carbon black and silica, a silane coupling agent, and a softening agent, followed by drying to obtain a rubber master batch (MB) containing silica or a mixture of carbon black and silica, adding to this a polybutadiene or styrene-butadiene copolymer rubber (R) having a Tg at least 10° C. higher than the Tg of the starting rubber in the silica or carbon black and silica mixture-rubber master batch (MB), and mixing by an internal mixer, wherein the ratio FMB/FCOM of the concentration FMB of the silica or the mixture of carbon black and silica based upon the rubber in the silica or carbon black and silica mixture-rubber master batch (MB) and the concentration FCOM of the silica or the mixture of carbon black and silica based upon the rubber in the rubber composition (COM) obtained by mixing in the internal mixer is 1.2 to 3.0.