The present invention relates to a cross-linkable or cross-linked rubber composition which is usable to constitute a tire tread having improved wear resistance, to such a tread and to a tire incorporating this tread. A rubber composition according to the invention comprises a diene elastomer of a number-average molecular weight Mn of less than 2000 g/mol which has a glass transition temperature Tg of greater than -25.degree. C., and it is such that said elastomer comprises one or more units resulting from the polymerisation of a vinylaromatic monomer, such as styrene. The invention applies in particular to tires of passenger-vehicle type.