This paper addresses the network-based leader–following consensus problem for the second-order multi-agent systems with nonlinear dynamics. Based on the Lyapunov–Krasovskii theory, a new delay-dependent sufficient condition in terms of linear matrix inequalities (LMIs) is presented to guarantee the consensus of the multi-agent system, and a sufficient condition for network-based controller design is proposed to ensure the followers reach consensus with the leader for second-order multi-agent systems with nonlinear dynamics. The effectiveness and applicability of the suggested solution is evaluated and verified through the simulation of two numerical examples.