The present invention relates to a vulcanizable rubber composition which can be used for the manufacture of tires. The invention also provides for a tire, the tread of which comprises such a composition. The rubber composition posses improved hysteresis and physical properties in the vulcanized state, while retaining satisfactory processing properties in the non-vulcanized state. The rubber composition comprises a reinforcing white filler and a diene block copolymer which is intended to interact with the white filler, the block copolymer comprising a diene block polymer having on at least one chain end thereof a polyether block having a molecular weight of between 1000 g/mol and 3000 g/mol, the polyether block corresponding to the formula: OnullCH2nullCH2nullO)nnullR,nullnull(I) in which n is an integer other than zero and R is a saturated or unsaturated hydrocarbon.