Abstract: In this paper, we investigate the problem of consensus in leader-following multi-agent system, where the information of the leader is only accessed by a subset of the following agents. For the part of the follower who cannot obtain the leader’s information, the state of the leader need to be estimated. In addition, considering the discontinuity of obtaining the output information of agents under certain conditions, an impulsive observer is introduced to reduce the sampling times among multiple agents. To achieve this, this paper aims to design a controller based on impulsive observer to achieve the consensus of leader-following multi-agent systems. Firstly, an impulsive full-order observer and a consensus protocol are designed for each follower, so that the follower can use the observer to estimate the leader. Secondly, the dynamic equation of the error system is derived, and the appropriately Lyapunov function is constructed by using the error variables. Finally, the stability of error systems is studied by using the Lyapunov stability theory combining with the linear matrix inequalities, so that the sufficient conditions for the leader-following consensus problem of multi-agent systems can be obtained. Numerical simulation results clearly show the effectiveness of the proposed controller.