The quick construction of the Shortest Path Tree (SPT) is essential to achieve fast routing speed for an interior network using link state protocols, such as OSPF and IS-IS. Whenever the network topology changes, the old SPT must be updated. In a network with a large number of nodes, the technology with the whole SPT re-computation by traditional static algorithms is very inefficient. It will take tremendous computation time and make routing table instability by unnecessary changes in an existing SPT. In this paper, we propose an improved algorithm for the dynamic SPT update to solve the above problems. The proposed algorithm is based on the understanding of the dynamic update process to reduce redundancy. Only significant edges that contribute to the construction of the new SPT will be considered. The analysis of the algorithm complexity and experimental results shows that our algorithm is much better than any others in the literature.