Abstract: The present invention relates to star-block interpolymers having the following structure (X—Y)n—C, wherein X represents a random copolymer block derived from conjugated diene and monovinyl aromatic monomer; Y represents a polyconjugated diene block; C represents a residue derived from a multifunctional lithium based initiator; and n represents the functionality of the initiator and has a value of not less than 3; and preparation of the same. The star-block interpolymers according to the present invention have in the same molecule both a random copolymer block derived from conjugated diene and monovinyl aromatic monomer and a rubber block selected from the group consisting of a homopolymer block derived from conjugated diene, a tapered copolymer block derived from conjugated dienes, a random copolymer block derived from conjugated dienes and combinations thereof, and hence possess excellent properties of the both kinds of rubbers, and can be used widely as elastomeric materials.