In　this　paper,　we　consider　a　generalized　longest　common　subsequence　problem　with　multiple　subsequence　inclusive　constraints.　For　the　two　input　sequences　X　and　Y　of　lengths　n　and　m,　and　a　set　of　d　constraints　P　=　{P　1　,…,　P　d　}　of　length　l　i　for　each　P　i　∈　P,　the　problem　is　to　find　a　common　subsequence　Z　of　X　and　Y　including　each　of　constraint　string　in　P　as　a　subsequence　and　the　length　of　Z　is　maximized.　A　simple　dynamic　programming　algorithm　to　this　problem　is　presented　in　this　paper.　The　correctness　of　the　new　algorithm　is　demonstrated.　The　time　complexities　of　the　new　algorithm　is　O(nmdt),　where　(Formula　presented.).　©　Springer　International　Publishing　Switzerland　2015.