Submodular　maximization　is　of　great　significance　as　it　has　included　many　classical　combinatorial　problems.　In　this　paper,　we　consider　the　maximization　of　the　sum　of　a　supermodular　function　and　a　monotone　DR-submodular　function　on　the　integer　lattice.　As　our　main　contribution,　we　present　a　streaming　algorithm　under　the　assumption　that　the　optimum　is　known,　and　a　two-pass　streaming　algorithm　in　general　case.　The　proposed　algorithms　are　proved　to　have　polynomial　time　and　space　complexity,　and　a　performance　guarantee　dependent　on　the　curvature　of　the　supermodular　function.