The　electron　emission　properties　of　lanthanum　hexaboride　(LaB6)　have　received　much　attention　because　its　low　work　function,　low　volatility,　high　brightness,　thermal　stability　and　high　mechanical　strength.　However,　single　crystal　LaB6　is　an　ideal　thermionic　emission　and　field　emission　cathode　material,　its　different　crystal　surfaces　exhibit　different　emission　properties.　So　far　the　physical　factors　of　the　emission　properties　of　different　crystal　surfaces　of　LaB6　single　crystal　have　been　rarely　reported.　In　this　paper,　the　density　function　theory　based　first-principles　calculations　are　used　to　analyze　the　electron　density　differences,　band　structures　and　densities　of　states　of　the　typical　LaB6　(100),　(110),　(111),　(210),　(211)　and　(310)　surfaces,　and　the　thermionic　emission　properties　of　the　high-quality　single　crystal　LaB6　typical　surfaces　are　tested.　The　theoretical　calculation　results　show　that　single　crystal　LaB6　has　metal　properties,　electron　emission　characteristics　and　anisotropy　of　emission　performance　which　are　mainly　caused　by　different　crystal　structures　and　electronic　structures　of　LaB6　typical　surfaces.　The　densities　of　La　atoms　in　different　surfaces　of　LaB6　single　crystal　are　different,　and　a　high　density　of　La　atoms　in　a　surface　is　beneficial　to　its　emission　performance.　The　difference　between　relative　positions　for　the　Fermi　level　of　different　surfaces　has　different　effect　on　their　emission　performance,　and　a　surface　with　high　position　of　Fermi　level　against　the　bottom　of　conduction　band　could　have　small　work　function　and　good　emission　performance.　In　addition,　a　surface　structure　of　single　crystal　LaB6　has　a　large　density　of　states　and　a　high　number　of　distributions　of　conduction　band　near　the　Fermi　level,　which　are　in　favor　of　its　electron　emission.　The　(100)　surface　of　single　crystal　LaB6　with　the　highest　density　of　La　atoms　and　electronic　structure　in　favor　of　electron　emission　could　have　optimal　electron　emission　performance　compared　with　the　remaining　crystal　surfaces.　Thermionic　emission　test　results　show　that　maximum　emission　current　densities　of　the　(100),　(110),　(111),　(210),　(211)　and　(310)　surfaces　are　42.4,　36.4,　18.4,　32.5,　30.5　and　32.2　A/cm(2)　at　the　cathode　temperature　1773　K　and　the　voltage　1　kV.　The　(100)　surface　of　LaB6　single　crystal　has　a　maximum　emission　current　density　under　the　same　test　condition,　meaning　that　this　surface　has　a　smallest　work　function　and　best　emission　property　compared　with　the　other　crystal　surface.　The　thermionic　emission　test　results　show　that　the　actual　performances　are　basically　accordant　with　the　calculated　results,　demonstrating　that　the　first　principle　calculation　could　provide　a　good　theoretical　guidance　for　studying　the　electron　emission　properties　of　rare　earth　hexaborides　(REB6)　and　other　cathode　materials.