PURPOSE: To obtain a detector for previously detecting the gradient of surface on which a vehicle travels by holding a received altitude data while relating to an absolute coordinate and then calculating the gradient between coordinates of a memory means for holding the road data in the form of absolute coordinate sequence or relative coordinate sequence.

CONSTITUTION: A navigation controller 1 is connected with a map information memory 10, a GPS receiver 12 for detecting current positional information, an oscillation gyro 14 for detecting the azimuth, etc. A travel controller for vehicle, i.e., a transmission controller 2, is also connected through a communication line and a gradient detected by a gradient detector is outputted to the controller 2. The memory 10 stores a road network data comprising an intersection data, a node data, and a road data. An altitude is stored for every intersection on the road and when the position of vehicle and the altitude are detected on the road, gradient of the road is calculated based on the distance between the current position and next intersection and the difference of altitude.