In　this　paper,　we　present　a　simple　polynomial　time　algorithm　for　a　generalized　longest　common　subsequence　problem　with　multiple　substring　exclusion　constraints.　The　problem　was　declared　to　be　NP-　hard,　but　we　finally　found　that　this　is　not　true.　A　new　polynomial　time　solution　for　this　problem　is　presented　in　this　paper.　The　correctness　of　the　new　algorithm　is　proved.　The　time　complexity　of　our　algorithm　is　analysed.　©　Springer　International　Publishing　Switzerland　2015.