This paper considers the straight-line trajectory tracking control problem of a class of underactuated underwater vehicles with bounded disturbances and hard input constraints. A constrained robust straight-line tracking controller based on model predictive control (MPC) is designed, and an event-triggered scheduling strategy is incorporated to alleviate the computation load of MPC. Furthermore, sufficient conditions for ensuring feasibility and closed-loop stability of the event-triggered MPC strategy are presented. Finally, numerical simulations demonstrate the efficacy of the proposed controller.