The crystal structures and properties of hafnium hydride under pressure are explored using the first-principles calculations based on density function theory. The material undergoes pressure-induced structural phase transition I4/mmm→Cmma→P21/m at 180 and 250 GPa, respectively, and all of these structures are metallic. The superconducting critical temperature Tc values of I4/mmm, Cmma, and P21/m are 47–193 mK, 5.99–8.16 K and 10.62–12.8 K at 1 atm, 180 and 260 GPa, respectively. Furthermore, the bonding nature of HfH2 is investigated with the help of the electron localization function, the difference charge density and Bader charge analyses, which show that HfH2 is classified as a ionic crystal with the charges transferring from Hf atom to H.