A rubber composition comprising: a block copolymer comprising a polymer block (a-1) comprising a structural unit derived from a conjugate diene compound and a structural unit derived from an aromatic vinyl compound and a polymer block (a-2) comprising a structural unit derived from a conjugate diene compound; or a structural unit derived from a conjugate diene compound and a structural unit derived from an aromatic vinyl compound, at least one polymer selected from natural rubber, isoprene rubber, butadiene rubber, a styrene-butadiene rubber other than the above block copolymer, an ethylene-α-olefin copolymer rubber, an ethylene-α-olefin-diene copolymer rubber, an acrylonitrile-butadiene copolymer rubber, chloroprene rubber, and a halogenated butyl rubber, wherein the polymer is incompatible with the polymer block (a-1) and is compatible with the polymer (a-2), and at least one filler selected from silica and carbon black, wherein a glass transition temperature of the polymer block (a-2) is lower than a glass transition temperature of the polymer block (a-1) in the block copolymer; the block copolymer has at least one functional group selected from the group consisting of an amino group, an imino group, a pyridyl group, a piperazyl group, and a thiol group or a functional group obtained by subjecting each of these functional groups to onium salt formation, a hydrocarbyloxysilyl group, or a silanol group in the end of the polymer block (a-2) side; the block copolymer has two glass transition temperatures separated from each other by 5°C or more within a range of -100 to 20°C by measurement in accordance with ASTM D3418; and the ratio of the block copolymer is 10% by mass or more when the sum of the block copolymer and the polymer is taken as 100% by mass, wherein, of the two glass transition temperatures in the block copolymer, one is a glass transition temperature of the polymer block (a-1) and the other one is a glass transition temperature of the polymer block (a-2) and the glass transition temperature of the polymer block (a-1) is from -60 to 20°C and the glass transition temperature of the polymer block (a-2) is from -100 to -30°C. a block copolymer comprising a polymer block (a-1) comprising a structural unit derived from a conjugate diene compound and a structural unit derived from an aromatic vinyl compound and a polymer block (a-2) comprising a structural unit derived from a conjugate diene compound; or a structural unit derived from a conjugate diene compound and a structural unit derived from an aromatic vinyl compound, at least one polymer selected from natural rubber, isoprene rubber, butadiene rubber, a styrene-butadiene rubber other than the above block copolymer, an ethylene-α-olefin copolymer rubber, an ethylene-α-olefin-diene copolymer rubber, an acrylonitrile-butadiene copolymer rubber, chloroprene rubber, and a halogenated butyl rubber, wherein the polymer is incompatible with the polymer block (a-1) and is compatible with the polymer (a-2), and at least one filler selected from silica and carbon black, wherein a glass transition temperature of the polymer block (a-2) is lower than a glass transition temperature of the polymer block (a-1) in the block copolymer; the block copolymer has at least one functional group selected from the group consisting of an amino group, an imino group, a pyridyl group, a piperazyl group, and a thiol group or a functional group obtained by subjecting each of these functional groups to onium salt formation, a hydrocarbyloxysilyl group, or a silanol group in the end of the polymer block (a-2) side; the block copolymer has two glass transition temperatures separated from each other by 5°C or more within a range of -100 to 20°C by measurement in accordance with ASTM D3418; and the ratio of the block copolymer is 10% by mass or more when the sum of the block copolymer and the polymer is taken as 100% by mass, wherein, of the two glass transition temperatures in the block copolymer, one is a glass transition temperature of the polymer block (a-1) and the other one is a glass transition temperature of the polymer block (a-2) and the glass transition temperature of the polymer block (a-1) is from -60 to 20°C and the glass transition temperature of the polymer block (a-2) is from -100 to -30°C.