The structure and properties of high-pressure phases of iron nitrides Fe7N3 in the pressure range of 50–150 GPa have been studied with ab initio calculations within the electron density functional theory. A new phase Amm2-Fe7N3, which is the most energetically favorable in the pressure range of 43–128 GPa, has been found using the USPEX (Universal Structure Predictor: Evolutionary Xtallography) algorithms. It has been thermodynamically shown that another high-pressure phase β-Fe7N3 is isostructural to a similar phase of iron carbide. The elastic properties have been calculated for all modifications ε-, β-, and Amm2-Fe7N3 stable at high pressures.