A star-shaped copolymer consisting of a hyperbranched poly (3-methyl-3-oxetanemethanol) core and polytetrahydrofuran arms was obtained by a one-step cationic copolymerization of 3-methyl-3-oxetanemethanol with tetrahydrofuran initiated by BF3 . OEt2. Tetrahydrofuran served as a solvent at the earlier stage of the polymerization. After 3-methyl-3-oxetanemethanol was exhausted essentially, the resulting hyperbranched species acted as a macro-initiator, and initiated the cationic polymerization of tetrahydrofuran. This can be attributed to the large difference in reactivities of the monomers.