A process for producing a conjugated diene copolymer rubber which comprises initiating a copolymerization reaction in a reaction system containing a first conjugated diene compound and a first aromatic vinyl compound and completing the reaction, adding a first polyfunctional monomer to the reaction system, optionally further adding a second conjugated diene compound and a second aromatic vinyl compound, and further conducting copolymerization reaction, and adding a modifier to the reaction system to react the modifier with the copolymer. A rubber composition having excellent processability, exhibiting sufficient hardness even after vulcanization, and possessing reduced rolling resistance can be obtained.