A profile of a designated road by which a vehicle is guided to a destination is predicted by road map data. In the case where it is difficult for the own vehicle to pass through a curve of the designated road ahead of the own vehicle, a warning is given to a driver or vehicle speed is automatically reduced. Whether or not the car is correctly running on the designated road is decided by deviation .DELTA..theta. (=.theta..sub.V -.theta..sub.M) between azimuth angle .theta..sub.V of the actual advancing direction of the own vehicle and azimuth angle .theta..sub.M of the designated road. When it is decided that there is a possibility that the own vehicle is running off the designated road, the warning is given or automatic speed reduction is stopped or suppressed. Due to the foregoing, it is possible to prevent the own vehicle from being improperly controlled and it becomes possible for a driver from feeling a sense of incongruity.