This paper presents an event-triggered model predictive control scheme for distributed linear systems with additional disturbances. The subsystem states are coupled with each other and affected by unknown bounded disturbances. The communication among subsystems is assumed to be prompt and free from any information loss. A novel distributed event-triggered strategy is developed to balance communication resources and system control performance during asynchronous communication. This mechanism is meticulously designed to ensure optimal system performance while utilizing communication resources. The nominal system is introduced to construct a local optimization problem and a triggering mechanism considering the coupling influence is developed. To counter the additional disturbances, the dual-mode control approach has been implemented along with developing a robust terminal set. The terminal set is purposefully designed to maintain system stability in the presence of additive disturbances, achieved through a meticulously designed triggering mechanism. Then it is imperative to discuss the stability of the resulting closed-loop system and provide a proof process of the feasibility of the iterative optimization. Finally, the effectiveness of the proposed algorithm is validated through simulation results, thereby confirming its efficacy.