Abstract To better clarify and understand the phase stability and elastic properties of stable Zr–Al binary intermetallic compounds, the structural properties, phase stability, elastic properties, and electronic structures of these compounds in Zr–Al system have been systematically investigated by using first-principles calculations. The calculated equilibrium structures and enthalpies of formation in present work are in good agreement with the available experimental and other theoretical data, and the results of enthalpies of formation show that ZrAl2 is the most stable. The elastic properties, including elastic constants, Poisson’s ratio and anisotropy index, and Debye temperatures were also investigated. It is found that ZrAl is the most anisotropic in Zr–Al binary compounds. Furthermore, the electronic structures were discussed to reveal the bonding characteristics of the compounds.