Rubber composition and vulcanized rubber

The invention provides a rubber composition and a vulcanized rubber which is obtained by uniformly mixing and vulcanizing the rubber composition. The rubber composition comprises a modified olefin polymer, the molecular chain of the modified olefin polymer comprises at least one monovinyl aromatic structure unit and at least two conjugated diene structure units, and the molecular chain of the modified olefin polymer further comprises a silane coupling agent structure unit having a formula (I) as shown in the specification, wherein the molecular weight of the modified olefin polymer is 50,000-1,000,000, R1-R4 are linear or branched C1-C20 alkyl or a heteroatom-containing straight or branched C1-C20 alkyl, and the heteroatom is halogen, oxygen, sulfur, silicon and/or phosphorus. The rubber composition is capable of balancing the relation between wet-skid resistance and rolling resistance effectively.