This article investigates the intermittent event-triggered optimal leader-following consensus for nonlinear multi-agent systems (MASs) utilizing the actor-critic algorithm. First, we propose a novel distributed intermittent event-triggered control strategy, and a sufficient criterion is obtained to guarantee the leader-following consensus of MASs by establishing a novel piecewise differential inequality. Next, the intermittent event-triggered optimal control strategy is delicately given. Remarkably, the optimality of MASs is proven based on policy iteration and the convergence of the closed-loop system is also proved based on the Lyapunov stability theory. Then, the intermittent event-triggered approximate optimal control strategy is designed via an actor-critic network whose weights are only updated at the trigger instants. Furthermore, the Zeno behavior can be excluded in this article. Finally, two simulation examples further verify the effectiveness of the proposed scheme.