The _∞ containment control problems for first-order multi-agent systems with multiple time-varying delays under directed network topology are investigated.Firstly, by introducing a convergence vector function, the _∞ containment control problems of multi-agent systems are transformed into the _∞ control problems of normal time-delay systems.Then, by using the Lyapunov stability theory, a suitable Lyapunov-Krasovskii functional is designed.Some sufficient conditions for _∞ containment control are established and the upper bound of the time-varying delays are obtained.Furthermore, the existence criterion of _∞ containment control performance constant is also gained when there is external disturbance in the multi-agent systems.Finally, simulations results show the effectiveness of the conclusions.