For controlling the multi-robot formation system, a general projection neural network based nonlinear model predictive control (NMPC) strategy is proposed in this paper. The multi-robot formation system consists of the trajectory tracking of leader robot and the leader-follower formation controlling. Their kinematic error systems can be reformulated as a convex nonlinear minimization problem by the NMPC method and can be transformed into a constrained quadratic programming (QP) optimization problem. To solve this QP problem online efficiently, a general projection neural network (GPNN) is applied to obtain the optimal solution, which includes the optimal inputs of the formation system. Compare to other existing leader-follower approaches, the proposed nonlinear MPC method can take the input and state constraints of system into consideration. In the end of this work, simulations of the trajectory tracking and multi-robot formation are performed to verify the effectiveness of the developed strategy.