This paper demonstrates that the idea of iterative learning control (ILC) can be applied to deal with the consensus problems for multi-agent systems. All agents are considered in directed networks and with higher-order discrete dynamics. It is shown that the multi-agent system can be enabled to achieve consensus at any desired state, and its process can be guaranteed to converge monotonically by selecting learning parameters appropriately. Furthermore, the ILC-based consensus protocols can provide sufficient robustness against network uncertainties. Simulation results are provided to verify the effectiveness of our theoretical study.