The invention relates to a process for the simplified preparation of a functionalized or nonfunctionalized diene block copolymer comprising at least one polyether block with a number-average molecular mass of substantially 150 to 5000 g/mol, linked to at least one block constituted of a diene elastomer by at least one silicon atom. The process according to the invention enables a high degree of grafting of the polyether onto the polymer chains. The present invention also relates to a reinforced rubber composition, in particular for the manufacture of tyres, comprising such a diene block copolymer which is intended to interact with the reinforcing filler. A rubber composition according to the invention has improved hysteresis properties in the vulcanized state, while at the same time conserving satisfactory working properties in the nonvulcanized state.