In this paper, we present a noble pattern synthesis method of linear and planar array antennas, with non-uniform spacing, for simultaneous reduction of their side-lobe level and pattern distortion during beam steering. In the case of linear array, the Gauss-Newton method is applied to adjust the positions of elements, providing an optimal linear array in the sense of side-lobe level and pattern distortion. In the case of planar array, the concept of thinned array combined with non-uniformly spaced array is applied to obtain an optimal two dimensional (2-D) planar array structure under some constraints. The optimized non-uniformly spaced linear array is extended to the 2-D planar array structure, and it is used as an initial planar array geometry. Next, we further modify the initial 2-D 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 constraints, minimizing the maximum side-lobe level of the 2-D planar array. It is shown that the proposed method can significantly reduce the pattern distortion as well as the side-lobe level, although the beam direction is scanned.