In　this　work,　we　employed　first-principles　calculations　to　investigate　the　stability,　electronic　structures,　mechanical　and　thermodynamic　properties　of　FexAlyCz　compounds　which　were　first　observed　in　Fe-Cr-B-Al-C　alloy.　The　results　reveal　that　the　FexAlyCz　compounds　are　thermodynamically　stable,　and　the　addition　of　C　element　improves　the　stability　of　FexAlyCz　compounds.　These　FexAlyCz　compounds　display　disparate　anisotropy　according　to　different　calculated　3D　curved　surfaces　of　Young＇s　modulus　and　anisotropic　index.　The　Fe3AlC　compound　has　the　biggest　shear　modulus,　bulk　modulus　and　Young＇s　modulus　with　the　values　of　141.2　GPa,　212.6　GPa　and　346.8　GPa,　respectively,　which　indicates　that　the　Fe3AlC　compound　has　the　largest　rigidity,　lateral　deformation　resistance　and　good　solid　compressibility　under　static　pressure.　The　ratio　of　G/B　shows　that　FeAl　and　Fe3AlC　are　brittle　phases,　while　the　Fe3Al　and　FeAl3　phases　appear　to　be　ductile.　The　calculated　electronic　structure　reveals　that　the　bonding　characteristics　of　the　FexAlyCz　compounds　are　the　mixture　of　both　metallic　and　covalent　bonds,　which　also　exhibits　anti-bond　effects.　The　Fe3AlC　compound　has　the　biggest　Debye　temperature　of　702.2　K.　Meanwhile,　the　hardness　of　Fe3AlC　is　19.4　GPa　which　is　three　times　of　the　Fe3Al　compound.　The　results　obtained　in　this　study　provide　a　theoretical　basis　for　the　applications　of　Fe3AlC　compound　in　Fe-Cr-B-Al-C　alloys.