The　concept　of　submodularity　has　wide　applications　in　data　science,　artificial　intelligence,　and　machine　learning,　providing　a　boost　to　the　investigation　of　new　ideas,　innovative　techniques,　and　creative　algorithms　to　solve　different　submodular　optimization　problems　arising　from　a　diversity　of　applications.　However　pure　submodular　problems　only　represent　a　small　portion　of　the　problems　we　are　facing　in　real　life　applications.　In　this　paper,　we　further　discuss　the　two-stage　submodular　maximization　problem　under　a　l-matroid　constraint.　We　design　an　approximation　algorithm　with　constant　approximation　ratio　with　respect　to　the　curvature,　which　improves　the　previous　bound.　In　addition,　we　generalize　our　algorithm　to　the　two-stage　submodular　maximization　problem　under　a　l-exchange　system　constraint.