Multi-agent system flocking control has been a research hot topic in recent years.In view of the problems that there remain oscillation and slow initial response in second-order flocking control systems, this paper proposes a flocking control algorithm incorporated higher-order artificial potential fields by integrating the general properties of artificial potential fields required for multi-agent systems.Viewing the potential field gradient as the deviation of the agent's expected position, the control law is designed from the perspective of trajectory tracking. And, the Hessian matrix of the artificial potential field is introduced into the flocking control, and an energy-based Lyapunov function is designed to prove out the stability of the flocking control method and the obstacle avoidance during the operation of the multi-agent system separately.Thenumerical simulation results show that the proposed high-order potential field method achieves a significant increase in the response speed of multi-agent flocking control, effectively suppressing the system oscillations.