In this paper, we design an optimal planar array geometry for maximum side-lobe reduction. The concept of thinned array is applied to obtain an optimal two dimensional(2-D) planar array structure. First, a 2-D rectangular array with uniform spacing is used as an initial planar array structure. Next, we modify the initial planar array geometry with the aid of thinned array theory in order to reduce the maximum side-lobe level. This is implemented by a genetic algorithm under some constraint, minimizing the maximum side-lobe level of the 2-D planar array. It is shown that the optimized planar array structure can achieve low side-lobe level without optimizing the excitations of the array antennas.