In an apparatus and method utilizing a navigation system for controlling a driving force to be exerted at an estimated position at which the vehicle is to pass to reach to a destination at which the vehicle is finally to reach, a running road estimating block estimates a future position of the own vehicle in which the vehicular driving force controlling apparatus is mounted on the basis of a present position of the own vehicle. The estimated future position is a point of a road for the vehicle to pass several seconds after a time at which the own vehicle is placed at the present position specified from a recorded content of an electronic road map stored in, for example, CD-ROM. A driving force predicting block determines a present vehicular load state derived by a running resistance measuring block as a required driving force at the estimated position by correcting the present vehicular load state by a height difference between the estimated position and the present position. A driving system controlling block changes a setting of an engine and/or automatic power transmission according to a magnitude of the required driving force at the present position.