Zirconium (Zr) is a strong metal with superior physical and chemical properties such as extreme resistance to heat and corrosion. Zr metal can undergo a series of structural transitions induced by temperature and/or pressure. Here, we employ density functional theory (DFT) to study high-pressure Zr. In particular, we compute its structural and mechanical properties for the α, β, and ω phases, in the pressure range of 0-70 GPa. Among them, the bcc-structured β phase is found to exhibit the lowest enthalpy above ~30 GPa, and it is mechanically stable up to the highest pressure under study. The calculation results are in good agreement with the corresponding high-pressure equation-of-state measurements in diamond anvil cells. Our study shows that DFT is an overall efficient and reliable first-principles method for predicting the properties of Zr metal, which has promising applications in extreme temperature and pressure environments.