The global structure stability of the impact-induced tensile waves mentioned by Huang (Huang, S. J. Impact-induced tensile waves in a kind of phase-transforming materials. IMA Journal of Applied Mathematics, 76, 847–858 (2011)) is considered. By introducing Riemann invariants, the governing equations of motion are reduced into a 2×2 diagonally strictly hyperbolic system. Then, with the aid of the theory on the typical free boundary problem and maximally dissipative kinetics, the global structure stability of the impact-induced tensile waves propagating in a phase-transforming material is proved.