We　consider　the　max　hypergraph　3-cut　problem　with　limited　unbalance　(MH3C-LU).　The　objective　is　to　divide　the　vertex　set　of　an　edge-weighted　hypergraph　H　=　(V,　E,　w)　into　three　disjoint　subsets　V-1,　V-2,　and　V-3　such　that　the　sum　of　edge　weights　cross　different　parts　is　maximized　subject　to　parallel　to　V-i　vertical　bar　-　vertical　bar　V-l　parallel　to　＜=　B　(for　all　i　not　equal　l　not　equal　l　is　an　element　of{1,　2,　3})　fora　given　parameter　B.　This　problem　is　NP-hard　because　it　includes　some　well-known　problems　like　the　max　3-section　problem　and　the　max　3-cut　problem　as　special　cases.　We　formulate　the　MH3C-LU　as　a　ternary　quadratic　program　and　present　a　randomized　approximation　algorithm　based　on　the　complex　semidefinite　programming　relaxation　technique.