MOMPA: multi-objective marine predator algorithm. In this paper, a multi-objective version of the recently proposed marine predator algorithm (MPA) is presented, which is called the multi-objective marine predator algorithm (MOMPA). In this algorithm, an external archive component is introduced to store the non dominated Pareto optimal solutions found so far. Based on the elite selection method, a top predator selection mechanism is proposed, which selects the effective solutions from the archive as the top predators to simulate the predator’s foraging behavior. The CEC2019 multi-modal multi-objective benchmark functions are utilized to evaluate the performance of the proposed algorithm and compared with nine state-of-the-art multi-objective meta-heuristics algorithms. In addition, seven multi-objective engineering design problems (car side impact problem, gear train design problem, welded beam design problem, disk brake design problem, two bar truss design problem, spring design problem and cantilever beam design problem) are used to further verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed MOMPA algorithm not only provides very competitive results but also outperforms other algorithms.