<p>This paper presents a multi-objective model predictive control (MOMPC) algorithm to underactuated ship path following control while combining velocity assignment, and an event-triggered strategy is introduced to reduce the frequency of solving optimization problem, aimed at improving navigational safety and reducing communication burdens. First, an MOMPC algorithm is designed to track the desired path at a specified velocity by constructing a dynamic convex combinatorial form of the cost function, where a logistic function is involved to automatically assign weights to ensure path convergence as the primary objective and velocity assignment as a secondary objective. Additionally, an event-triggered strategy is introduced to reduce the computational burden while maintaining a satisfactory level of tracking performance. Finally, the simulation validates the effectiveness of the method.</p>