Novel energetic thermoplastic elastomers (TPEs) based on tetrahydrofuran (THF) and 3,3-bis(azidomethyl) oxetane (BAMO) were prepared in this present study by cationic living polymerization. A bifunctional catalyst, triflic anhydride [(CF3SO2)2O] was selected to be an initiator for the polymerization THF and BAMO. The resulting polymers were characterized by IR, NMR, and DSC, which demonstrated that triblock copolymers with A-B-A type were formed. The polymers were indicated from thermogravimetric analysis (TGA) to have decomposed at approximately 243-degrees-C. The decomposition enthalpies were determined by DSC. These enthalpies were varied with the poly-BAMO contents of the copolymers. The synthesized polymers exhibited relatively good mechanical properties and thermoplastic characteristics at room temperature.