A sulphur-vulcanizable rubber composition usable for the manufacture of tires, based on at least: (A)--one diene elastomer selected from the group consisting of polybutadienes, natural rubber, synthetic polyisoprenes, butadiene copolymers, isoprene copolymers and mixtures of these elastomers (component A); (B)--a reinforcing white filler (component B); (C)--a coupling agent (white filler/diene elastomer) bearing at least one activated double ethylene bond (component C), with which there is associated: (D)--between 0.05 and 1 phr (parts by weight per hundred of elastomer) of a heat-triggered radical initiator (component D).The coupling agent is in particular an alkoxysilane of the family of alkoxy(C.sub.1 C.sub.4)-silylpropyls, in particular a trialkoxy(C.sub.1 C.sub.4)-silylpropyl methacrylate, in particular trimethoxy-silylpropyl methacrylate. Process for preparing such a rubber composition. Tire or semi-finished product, in particular tread, for a tire comprising a rubber composition according to the invention.