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　is　an　element　of　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　t　=　Pi(1　＜=　i　＜=　d)　l(i).