A steering assist system includes traffic-line detecting means for detecting right and left traffic lines marked on a road, preceding-vehicle detecting means for detecting a preceding vehicle traveling ahead of a subject vehicle, traveling-target-point setting means for setting a traveling target point for traveling of the subject vehicle at a predetermined position in the preceding vehicle when the preceding vehicle is not within predetermined ranges from the right and left traffic lines, and for setting the traveling target point at a position offset from the predetermined position in the preceding vehicle toward the center of a traveling lane of the subject vehicle when the preceding vehicle is within the predetermined range of any one of the right and left traffic lines, and steering control means for controlling steering so that the subject vehicle passes over the traveling target point.