In this paper, the pattern synthesis of concentric elliptical antenna arrays (CEAAs) for effective antenna design is presented. The current amplitudes and angular positions values of the CEAA elements are optimally found by using the Marine Predators Algorithm (MPA) in order to obtain the optimum radiation pattern. The MPA method is a novel nature-based optimization algorithm that is inspired by ocean predators foraging strategy. The antenna arrays with reduced maximum side lobe levels (MSL) and narrowed half power beam widths (HPBW) are an efficient antenna with optimum radiation pattern to suppress interference and increase directionality. In addition, CEAAs with different numbers of elements are examined to show the flexibility and performance of the proposed algorithm in this study. For 18-element CEAA, MPA obtained the HPBW between 29.18 degrees and 31.34 degrees, and MSL between - 20.70 and - 25.89 dB. For 30-element CEAA, the optimum values of HPBW are between 20.13 degrees and 21.38 degrees, and the optimum values of MSL are between - 18.90 and - 20.50 dB. The results of pattern synthesis obtained by MPA are compared with other metaheuristic optimization methods, and it is seen that the results of the proposed method are generally better.