Based on the supercell structures of Fe-Cr-Mn alloys having the composition Fe18Cr6Mn8, the structural, electronic and magnetic properties of the alloys have been investigated using first-principle calculations, and the effects of dissolved nitrogen on the properties of Fe18Cr6Mn8 alloys have been further discussed. The Fe18Cr6Mn8 alloys were considered to have two different structures, Cr6Fe6Mn8Fe12 and Fe6Cr6Mn8Fe12. The lattice constants of cells Cr6Fe6Mn8Fe12 and Fe6Cr6Mn8Fe12 are similar to each other, however the octahedral volumes in the center of the cell (VO) differ. After nitrogen solid solution, the lattice constants and cell volumes of Fe18Cr6Mn8 alloys slightly increase, while the octahedral volume sees a large increase: 11.6% for Cr6Fe6Mn8Fe12 and 18.2% for Fe6Cr6Mn8Fe12. The Fe18Cr6Mn8 (N) alloys are of high stability. Solute atoms (N) increase the stability of the Fe18Cr6Mn8 system, and Cr6Fe6Mn8Fe12-N is more stable than Fe6Cr6Mn8Fe12-N. Besides N atoms with negative charges (obtaining electrons), Fe atoms in different sites also display different electronegativity. After nitrogen solid solution, the magnetic moment of Cr6Fe6Mn8Fe12 decreases about 20%, and that of Fe6Cr6Mn8Fe12 decreases about 79%. The ratio of bulk modulus B to shear modulus G (B/G ratio), representative of the ductility of the alloy, of Cr6Fe6Mn8Fe12 decreases about 15%, and that of Fe6Cr6Mn8Fe12 decreases about 30%. The addition of nitrogen decreases the Zener anisotropy ratios of Fe18Cr6Mn8, which shows the elastic anisotropy of Fe18Cr6Mn8N is lower than that of Fe18Cr6Mn8.