In nature, the motion of swarm intelligence has a regularity such as the line motion based bird migration, the circle motion based fish swarming, etc., which has important theoretical significance and vast application prospect in engineering practice. In this paper, we investigate the distributed encirclement control problem of a group of multi-agent systems. With considering the feature that each agent can achieve local target information, we design an averaging estimator to achieve the target information, and propose a distributed control scheme to achieve the encirclement and keep the formation changing with the target states. By Lyapunov theory analysis, it is proved that each individual agent can achieve the information about the marked arerage position in a finite time, encircle and pursue the targets based on the encirclement formation. Finally, a numerical example is presented to illustrate the obtained theoretical results.