This paper introduces a new algorithms for reconstructing the suffix tree of character string, when a substring id deleted from the string or a string is inserted into the string as a substring. The algorithem has two main functions, delete-structure and insert-structure. The main objective of this algorithm is to save the time for constructing the suffix tree of an edited string, when the suffix tree of the original string is available. We tested the performance of this algorithm with some DNA sequences. This test shows that delete-reconstructing can save time when the length of the subsequence deleted is less than 30% of the original sequence, and the insert-reconstructing takes less time with regard to the length of inserted sequence.