In　this　paper,　we　investigate　the　two-stage　submodular　maximization　problem,　where　there　is　a　collection　F={f1,…,fm}　of　m　submodular　functions　which　are　defined　on　the　same　element　ground　set　Ω.　The　goal　is　to　select　a　subset　S⊆Ω　of　size　at　most　such　that　[Formula　presented]　is　maximized,　where　I　denotes　a　specifically-defined　independence　system.　We　consider　the　two-stage　submodular　maximization　with　a　P-matroid　constraint　and　present　a　(1/(P+1))(1−1/e(P+1))-approximation　algorithm.　Furthermore,　we　extend　the　algorithm　to　the　two-stage　submodular　maximization　with　a　more　generalized　P-exchange　system　constraint　and　show　the　approximation　ratio　can　be　maintained　with　slightly　modifications　of　the　algorithm.　©　2020　Elsevier　B.V.