A navigation system in a vehicle stores position history information including position information related to a detection position detected by a position detector and position information related to a map matching position. The map matching position is obtained by matching the detection position with a point of a road in road map data. When the vehicle runs on a not-stored road that is not stored in the road map data, the navigation system determines a trail of running of the vehicle from departure from a stored road that is stored in the road map data to comeback into a stored road that is stored in the road map data, based on the stored position history information.