With the formation of structural vacancies, zirconium nitrides (key materials for cutting coatings, super wear-resistance, and thermal barrier coatings) display a variety of compositions and phases featuring both cation and nitrogen enrichment. This study presents a systematic exploration of the stable crystal structures of zirconium heminitride combin-ing the evolutionary algorithm method and ab initio density functional theory calculations at pressures of 0 GPa, 30 GPa, 60 GPa, 90 GPa, 120 GPa, 150 GPa, and 200 GPa. In addition to the previously proposed phases P42/mnm-, Pnnm-, and Cmcm-Zr2N, five new high-pressure Zr2N phases of P4/nmm, I4/mcm, P21/m, Pˉ3m1, and C2/m are discovered. An en-thalpy study of these candidate configurations reveals various structural phase transformations of Zr2N under pressure. By calculating the elastic constants and phonon dispersion, the mechanical and dynamical stabilities of all predicted structures are examined at ambient and high pressures. To understand the structure-property relationships, the mechanical properties of all Zr2N compounds are investigated, including the elastic moduli, Vickers hardness, and directional dependence of Young's modulus. The Cmcm-Zr2N phase is found to belong to the brittle materials and has the highest Vickers hardness (12.9 GPa) among all candidate phases, while the I4/mcm-Zr2N phase is the most ductile and has the lowest Vickers hard-ness (2.1 GPa). Furthermore, the electronic mechanism underlying the diverse mechanical behaviors of Zr2N structures is discussed by analyzing the partial density of states.