The　high　quality,　high　purity　and　large　size　LaB6,　CeB6　single　crystals　had　been　successfully　grown　by　optical　floating　zone　method.　Each　parameter　which　impact　in　the　process　of　crystal　growth　was　studied　in　this　article.　We　determine　the　optimum　crystal　growth:　(1)　LaB6:　speed　of　30　r/min,　the　growth　rate　of　8-10　mm/h,　twice　zone　melting;　(2)　CeB6:　speed　of　30　r/min,　the　growth　rate　of　15-20　mm/h,　once　zone　melting.　And　then　analysis　the　characterizations　of　single　crystals.　We　use　the　main　method,　and　they　are　single　crystal　diffraction,　Raman　diffraction,　rocking　curve,　cross-section　scanning.　These　show　that　floating　zone　growth　is　the　best　method　in　the　produced　single　crystal　REB6　(LaB6,　CeB6)　cathode.