In this paper, a multi-step ahead prediction algorithm of link travel speeds has been developed using a Kalman filtering technique in order to calculate a dynamic shortest path. The one-step and the multi-step ahead link travel time prediction models for the calculation of the dynamic shortest path have been applied to the directed test network that is composed of 16 nodes: 3 entrance nodes, 2 exit nodes and 11 internal nodes. Time-varying traffic conditions such as flows and travel time data for the test network have been generated using the CORSIM model. The results show that the multi-step ahead algorithm is compared more favorably for searching the dynamic shortest time path than the other algorithm.