In this paper, to obtain antenna arrays with grating lobes suppression capability in wideband and achieve a low peak sidelobe level (PSLL), two non-uniform spiral antenna arrays and an enhanced Harris Hawks optimization (EHHO) algorithm are proposed. By controlling the parameters of the spiral line and sampling equidistant on the spiral line, the sampling points that make up the non-uniform array can be arranged in the plane uniformly and non-uniformly. The simulation results indicate that, because of this special arrangement, the non-uniform arrays obtain the capability of grating lobe suppression in wideband or wide spacing arrangement when compared to the classic uniform array. In addition, to obtain lower PSLL, the Harris Hawks optimization (HHO) algorithm is used for array synthesis because of its diversity of search methods. By employing the step-type taper distribution strategy and the migration strategy, the algorithm’s search ability is enhanced, and the simulation results indicate the EHHO algorithm obtains a better solution in terms of the PSLL than other algorithms. A simple patch antenna is designed to build the non-uniform spiral arrays synthesized by the EHHO algorithm. The calculation and simulation results validate the superior performance of the proposed algorithm.