Studies have been made for the purpose of achieving both the improvement in the storage stability of a solution-polymerized diene rubber that is modified with an alkoxysilane compound and the improvement in the physical properties of the diene rubber when blended with silica. Thus, a production method whereby it becomes possible to produce a modified solution-polymerized diene rubber having good storage stability and high reactivity with silica is developed, by introducing several tens percent of a three blanched or four blanched component that has been coupled with a tin compound into a modified solution-polymerized diene rubber, then coagulating the resultant alkoxysilane modified diene rubber with steam and then drying the coagulated product. In addition, the physical properties of the rubber are further improved successfully by introducing a highly reactive structure to a polymerization initiation terminal of the rubber in the polymerization of the rubber using an alkyl lithium as a polymerization initiator.