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The phase stability of the hafnium dioxide compounds HfO _2 , a novel material with a wide range of application due to its versatility and biocompatibility, is predicted to be achievable by using evolutionary technique, based on first-principles calculations. Herein, the candidate structure of HfO _2 is revealed to adopt a tetragonal structure under high-pressure phase with P4/nmm space group. This evidently confirms the stability of the HfO _2 structures, since the decomposition into the component elements under pressure does not occur until the pressure is at least 200 GPa. Moreover, phonon calculations can confirm that the P4/nmm structure is dynamically stable. The P4/nmm structure is mainly attributed to the semiconducting property within using the Perdew–Burke–Ernzerhof, the modified Becke-Johnson exchange potential in combination with the generalized gradient approximations, and the quasi-particle GW approximation, respectively. Our calculation manifests that the P4/nmm structure is likely to be metal above 200 GPa, arising particularly from GW approximation. The remarkable results of this work provide more understanding of the high-pressure structure for designing metal-oxide-based semiconducting materials.