A terminal-modified polymer is manufactured by performing a polymerization reaction of a vinyl aromatic monomer, a conjugated diene monomer or both in the presence of an anionic polymerization initiator: and then adding an alkoxy aluminum compound thereinto to terminate the polymerization reaction. Alternatively, a terminal-modified polymer can also be manufactured by adding an aluminum halide compound instead of the alkoxy aluminum compound to terminate the polymerization reaction, and allowing for a reaction with a lower alcohol having 1 to 4 carbon atoms. The resulting terminal-modified polymer can improve the dispersibility of silica used as a compounding agent in rubber compositions for automobile pneumatic tires and the like.