A driving assist apparatus for a vehicle which calculates a path by an algorithm suitable for real-time path calculation in a vehicle-installed computing device is provided. A basic path that changes the deflection angle of the vehicle to 0 is computed from an initial vehicle position. From the basic path, a target path is computed, for example, by adding straight-line paths to the two opposite ends of the basic path. On the basis of the target path, a driving assist is performed. During the driving assist, a basic path is re-calculated. If it is determined that a similarity-enlarged path obtained through similarity enlargement of the basic path can be used to reach the target position point, a target path is re-set on the basis of the similarity-enlarged path. Then a driving assist is performed on the basis of the re-set target path.