Let　E　be　a　proper　class　of　triangles　in　a　triangulated　category　C;　and　let　(A,　B,　C)　be　a　recollement　of　triangulated　categories.　Based　on　Beligiannis＇s　work,　we　prove　that　A　and　C　have　enough　E-projective　objects　whenever　B　does.　Moreover,　in　this　paper,　we　give　the　bounds　for　the　E-global　dimension　of　B　in　a　recollement　(A,　B,　C)　by　controlling　the　behavior　of　the　E-global　dimensions　of　the　triangulated　categories　A　and　C:　In　particular,　we　show　that　the　finiteness　of　the　E-global　dimensions　of　triangulated　categories　is　invariant　with　respect　to　the　recollements　of　triangulated　categories.