A vehicle driving assist apparatus for guiding a vehicle to a target position is provided. A basic path that changes the deflection angle .theta. to 0 is determined, and is subjected to similarity transformation. On the basis of the similarity-transformed path, a path factoring in transition from the initial steering angle is set. Then, a correction is made such that the area in the running distance-curvature graph regarding this path becomes equal to a corresponding area regarding the basic path, thereby setting a corrected path. The corrected path is similarity-transformed, and then is re-corrected in accordance with transition from the initial steering angle. Thus, a final target path is obtained.