Combined with artificial potential field (APF) method, an adaptive leader-following formation control with collision avoidance strategy is developed for a class of second-order nonlinear multi-agent systems. Since nonlinear dynamic systems contain the inherent complexities and uncertainties, most formation control with collision avoidance objectives are focused on linear multi-agent systems. In order to solve the problems of unknown nonlinear dynamics, neural network (NN) is employed in the proposed formation protocol design. In any formation control, the higher probability of collision among agents is taken place in the initial stage. The proposed method effectively solves the problems by integrating APF method into leader-following formation strategy. Based on the Lyapunov stability theory and graph theory, the second-order nonlinear multi-agent systems can achieve an ideal formation pattern with the collision avoidance performance. The numerical simulations are carried out to further verify the performance of the proposed algorithm.