This paper investigates the distributed receding horizon control (RHC) problem of a vehicle platoon with nonlinear dynamics and subject to system constraints, where each vehicle can communicate with its immediate predecessor and follower. A novel optimization problem and detailed distributed RHC algorithm are designed in order to keep a platoon formation, and further to ensure neighbor gamma-gain stability (which is a new notion proposed in this paper and generalizes the string stability). The sufficient conditions on ensuring closed-loop stability and neighbor gamma-gain stability are established, respectively. Finally, simulation studies are provided to verify the theoretical results. It is shown that it is possible to achieve certain control performance (i.e., gamma-gain stability) and keep a formation simultaneously for the nonlinear vehicle platoon using distributed RHC. (C) 2016 Elsevier Ltd. All rights reserved.