Let　V(D)=X∪Y　be　a　bipartition　of　a　directed　graph　D.　We　use　e(X,Y)　to　denote　the　number　of　arcs　in　D　from　X　to　Y.　Motivated　by　a　conjecture　posed　by　Lee,　Loh　and　Sudakov　(2016)　[16],　we　study　bipartitions　of　oriented　graphs.　Let　D　be　an　oriented　graph　with　m　arcs.　In　this　paper,　it　is　proved　that　if　the　minimum　degree　of　D　is　δ,　then　D　admits　a　bipartition　V(D)=V1∪V2　such　that　min⁡{e(V1,V2),e(V2,V1)}≥([Formula　presented]+o(1))m.　Moreover,　if　the　minimum　semidegree　d=min⁡{δ+(D),δ−(D)}　of　D　is　at　least　21,　then　D　admits　a　bipartition　V(D)=V1∪V2　such　that　min⁡{e(V1,V2),e(V2,V1)}≥([Formula　presented]+o(1))m.　Both　bounds　are　asymptotically　best　possible.　©　2018　Elsevier　Inc.