Most of the systems that rely on the solution of shortest path problem or constrained shortest demand real-time response to unexpected real world events that affect the input graph of the problem such as car accidents, road repair works or simply dense traffic. We developed new incremental algorithm that uses data already present in the system in order to quickly update a solution under new conditions. We conducted experiments on real data sets represented by road graphs of the cities of Oldenburg and San Joaquin. We test the algorithm against that of Muhandiramge and Boland [1] and show that it provides up to 50% decrease in computation time compared to solving the problem from scratch.