In this paper, a design problem of non-uniform single-ring circular antenna arrays (CAA) and concentric circular antenna array (CCAA) for maximum side lobe level (SLL) by a hybridized method based on gravitational search algorithm with differential evolution (GSADE) is dealt with. The algorithm is used to determine an optimal set of current excitation weights and antenna inter-element spacing for CAA and an optimal set of current excitation weights for CCAA that provide a radiation pattern with maximum reduction of SLL. The same algorithm has been applied successively on CAAs of 8, 10, and 12 elements and two 3-ring CCAA, one having the set of 4, 6, and 8 elements and the other having 8, 10, and 12 elements with and without center element. Experimental results show a considerable improvement of SLL and some restricted improvement of first null beamwidth (FNBW) and 3-dB beamwidth as well with respect to the corresponding uniform cases and those of some recent literature reported in this paper.