The phase stability of the hafnium dioxide compounds HfO2, a novelmaterial with a wide range of application due to its versatility and biocompatibility,is predicted to be achievable by using evolutionary technique, based on first-principlescalculations. Herein, the candidate structure of HfO2 is revealed to adopt a tetragonalstructure under high-pressure phase with P4/nmm space group. This evidentlyconfirms the stability of the HfO2 structures, since the decomposition into thecomponent elements under pressure does not occur until the pressure is at least200GPa. Moreover, phonon calculations can confirm that the P4/nmm structure isdynamically stable. The P4/nmm structure is mainly attributed to the semiconductingproperty within using the Perdew{Burke{Ernzerhof, the modified Becke-Johnsonexchange potential in combination with the generalized gradient approximations, andthe quasi-particle GW approximation, respectively. Our calculation manifests that theP4/nmm structure likely to be metal above 200GPa, arising particularly from GWapproximation. The remarkable results of this work provide more understanding ofthe high-pressure structure for designing metal-oxide-based semiconducting materials.