This paper presents a distributed multi-objective model predictive control (MPC) strategy for multi-objective control problems of nonlinear vehicle platoon systems subject to state and control constraints. Based on the predecessor-follower communication topology, the nonlinear longitudinal cruise control models of connected vehicle platoons are established. The lexicographic method is applied to formulate the distributed multi-objective optimization problem. Moreover, together with the triple elements of MPC, the constraints on string stability and contractive are designed to guarantee stability and string stability in the context of optimality of economic performance and coordination performance of the vehicle platoon. Finally, simulation results of typical conditions verify the effectiveness of the proposed scheme.