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This paper describes lateral and longitudinal control algorithms when vision-based autonomous vehicles form a platoon by detecting a preceding one with a machine vision system. The visual platooning is an extension of the longitudinal control in ACC, and is featured by both the lateral and longitudinal control of following vehicles. The lateral control algorithm for a following vehicle uses a target point positioned on a preceding vehicle and captured in the field of view. When the target point is appropriately positioned, a following vehicle is guided as if it chased the target. The origin of the lateral control algorithm is an algorithm for an automated vehicle with a localization function including the dead reckoning, named the target point following algorithm. The lateral control in the visual platooning consists of the steps of target point detection, path generation, and lateral control calculation.