This letter proposes a novel low complexity shortest path tree restoration scheme to address link cost perturbation problem for link state routing in IP Networks. The proposed scheme can reduce the number of unnecessary shortest path tree recomputations and also provides a low-complexity computation when the Shortest Path Tree (SPT) restoration process executes. The proposed scheme has been designed based on the Network Simplex Method (NSM) and Sensitivity Analysis (SA) techniques to perform the optimality test for the current shortest path tree. The computational overhead is compared with various dynamic schemes over six network benchmarks.