Abstract: In recent years, multi-agent systems have become one of the hot topics in the field of control research area due to their wide applications in chemical process system, transportation system, smart grid system, and so on. On the other hand, distributed predictive control (DPC) can effectively deal with the hard constraints and make use of the predictive information to estimate the interaction between subsystems in the future. However, for multi-agent systems with limited resources, traditional DPC based on time-triggered mechanism may cause unnecessary waste of resources, if the subsystems update the control laws periodically even if the performance of system has met the requirements. The event triggering mechanism working in a non-periodic way can balance resources consumption and systems performance effectively. In this paper, an event-triggered robust distributed predictive control strategy based on two-layer invariant sets is proposed for multi-agent systems subject to disturbances. Under the distributed control structure, the event-triggered predictive control optimization problem is established for each subsystem by means of the coupled cost function based on event triggered instant. By using the theory of input-to-state stability (ISS), the event-triggered condition is derived, which involves the subsystem's own information and the information from other neighbour subsystems. When the event-triggering condition is satisfied, the measurement state of subsystem is transmitted to the controller for solving the distributed predictive control optimization problem, and then, the information will be exchanged with neighbours. By introducing two-layer invariant sets, the robustness of the multi-agent systems with disturbances can be guaranteed and sufficient conditions are obtained for ensuring the recursive feasibility and system closed-loop stability. Finally, the proposed algorithm is simulated and the effectiveness is illustrated by a vehicle control system. It is shown from the simulation results that the proposed algorithm can reduce the computational and communication consumption without increasing the complexity of the DPC algorithm.