In this paper, the local flocking of multi-agent systems is investigated, which means all agents form some groups of surrounding multiple targets with the partial information exchange. For the purpose of realising local multi-flocking, a control algorithm of local flocking is proposed, which is a biologically inspired approach that assimilates key characteristics of flocking and anti-flocking. In the process of surrounding mobile targets through the control algorithm, all agents can adaptively choose between two work modes to depend on the variation of visual field and the number of pursuing agents with the mobile target. One is a flocking pursuing mode which is that some agents pursue each mobile target, the other is an anti-flocking searching mode that means with the exception of the pursing agents of mobile targets, other agents respectively hunt for optimal the mobile target with a closest principle between the agent and the target. In two work modes, the agents are controlled severally via the different control protocol. By the Lyapunov theorem, the stability of the second-order multi-agent system is proven in detail. Finally, simulation results verify the effectiveness of the proposed algorithm.