There are challenges in the production and application of rare-earth permanent magnet (PM) materials due to resource distribution, cost, environmental unfriendliness, and recycling difficulties. Thereby, the demand for high-performance rare-earth-free PMs has increased rapidly over the past decade. Body-centered tetragonal alpha ''-Fe16N2 is a promising candidate for future rare-earth-free PMs due to the low cost of Fe, environmental friendliness and high energy. In this work, the electronic structures and magnetic properties of body-centered tetragonal alpha ''-Fe16N2 are investigated by first-principles calculations. The total magnetic moments of alpha ''-Fe16N2 are 38.59 mu B per cell, equivalent to 2.41 mu B/Fe atoms. Through band and density of state analysis, alpha ''-Fe16N2 is found to present metallic and ferromagnetic character. The magnetocrystalline anisotropy energy (EMCA) of alpha ''-Fe16N2 is -0.66 J cm-3, showing perpendicular magnetic anisotropy (PMA). PMA can be mainly ascribed to the spin-orbit-coupling between (dz2, dyz) and (dxz, dyz) orbitals at the Fe(8h) site. The Curie temperature of alpha ''-Fe16N2 is 1369 K, which is larger than that of pure bcc-Fe (1023 K). Therefore, alpha ''-Fe16N2 possessing PMA and high Curie temperature is a potential rare-earth-free PM candidate material, which has application prospects in high temperature data storage devices, traction motors, wind turbines and power generating machines.