In this article, we consider a generalized longest common subsequence (LCS) problem with multiple substring inclusive constraints. For the two input sequences X and Y of lengths n and m, and a set of d constraints [Formula: see text] of total length r, the problem is to find a common subsequence Z of X and Y including each of constraint string in P as a substring and the length of Z is maximized. A new dynamic programming solution to this problem is presented in this article. The correctness of the new algorithm is proved. The time complexity of our algorithm is [Formula: see text]. In the case of the number of constraint strings is fixed, our new algorithm for the generalized LCS problem with multiple substring inclusive constraints requires [Formula: see text] time and space.