The　thermal　stabilities,　electronic　structures,　magnetic　properties　and　the　charge　transfers　of　the　rare　earth　Cerium　hexaborides　CeB6　under　isostatic　pressure　of　0　GPa　and　1　GPa　are　systematically　investigated　in　detail　within　the　framework　of　density　functional　theory　method　with　pseudopotential　approximation.　The　analyzing　results　show　that　the　Cerium　Boride　CeB6　under　1　GPa　has　relatively　lower　total　energy　of　-1526.1675　eV　than　that　of　Cerium　Boride　CeB6　under　0　GPa.　The　Cerium　Boride　CeB6　under　1　GPa　has　band　gap　of　1.305　eV,　which　is　0.152　eV　lower　than　that　of　the　Cerium　Boride　CeB6　under　0　GPa　of　1.457　eV.　The　work　function　of　electrons　is　also　decreased　by　0.465　eV.　There　are　three　energy　valleys　in　the　bottom　conduction　band　and　four　energy　peaks　in　the　top　valance　band,　the　emission　efficiency　should　be　high.　The　quantity　of　electrons　that　are　readily　to　be　motivated　for　emission　is　larger　for　Cerium　hexaborides　CeB6　under　1　GPa.　The　total　partial　density　of　states　for　Cerium　Boride　CeB6　under　different　isostatic　pressure　is　mainly　formed　by　B　p　electrons.　The　B　should　play　more　important　role　in　electron　emission　for　CeB6　under　1　GPa.　The　CeB6　under　different　isostatic　pressure　is　ferromagnetic　material.　The　combination　bond　effect　between　B　is　enhanced　for　Cerium　Boride　CeB6　under　1　GPa.