Summary In this paper, we consider the optimal topology for leader-following consensus problem of continuous-time and discrete-time multi-agent systems based on linear quadratic regulator theory. For the first-order multi-agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second-order multi-agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second-order leader-following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.