A re-routing apparatus and method for calculating an optimum path from a path deviated position to an original path in a navigation system, and a navigation system using this apparatus and method are disclosed. When a movable body traveling on a predetermined path provided from a navigation system has deviated from the path, links are selected which meet links extending in a direction having small accumulated travel cost from the deviated position link from among links included in the original path, and then paths traveling from the deviated position to the destination via the selected links are determined as re-routing paths. Accordingly, when the movable body has deviated from the predetermined path communication cost to connect with a server can be reduced and another deviation possibility due to time delay taken until new paths are provided can also be reduced by enabling the navigation terminal by itself to calculate the optimum path from the deviated position to the original path without connecting with the server.