Platooning is the desired group driving behavior of connected and autonomous vehicles on roads. As a platoon, autonomous vehicles by synchronizing their speed, maintain shorter headway and inter-vehicle distance. Platooning is more challenging when the size of the platoon becomes large as a swarm of vehicles platooning behavior simultaneously shall be synchronized. This paper proposes a differential game approach to vehicle swarm platooning. The connected vehicles can communicate but cannot enter into binding agreements. Each vehicle of the swarm is assigned with a convex cost function of its distance to the predecessor along with its control efforts to be minimized. It is shown that the vehicle swarm platooning as a noncooperative differential game admits a unique Nash equilibrium. A swarm's platooning behavior with the size of 20 vehicles has been investigated via simulations to justify the models and solutions.