The　online　optimization　has　been　extensively　studied　under　a　variety　of　different　settings.　In　this　paper,　we　consider　the　online　maximization　problems　with　stochastic　linear　cumulative　constraints,　where　the　objective　functions　are　the　sum　of.-weakly　DR-submodular　functions　and　concave　functions.　Inspired　by　the　penalty　function　strategy,　we　propose　an　algorithm　of　primal-dual　type　to　solve　this　class　of　problems.　Under　mild　conditions,　we　show　that　the　algorithm　achieves　sub-linear　regret　bounds　and　cumulative　budget　violation　bounds　with　high　probability.