A modified conjugated diene-based polymer rubber obtained by reacting, a siloxane compound having at least one ketimine group or aldimine group and at least two alkoxysilyl groups in a molecule to polymerization active ends of a polymer or copolymer obtained by solution polymerization of a conjugated diene monomer or a conjugated diene monomer and an aromatic vinyl compound monomer in the presence of an organic active metal catalyst and a rubber composition containing the modified conjugated diene-based polymer rubber and having an improved processability, heat buildup and abrasion resistance.