The process in which the migration of an axon growth cone is directed to a specific target site along the dorsal-ventral body axis in response to a combination of attractive and repulsive cues. The dorsal/ventral axis is defined by a line that runs orthogonal to both the anterior/posterior and left/right axes. The dorsal end is defined by the upper or back side of an organism. The ventral end is defined by the lower or front side of an organism.