A circularly polarized flat-topped beam is synthesized by concentric circular arrays of microstrip patch antennas using the particle swarm optimization (PSO). The beam synthesis is performed by controlling only the magnitudes of excitation of the array elements where all the array elements are excited in phase. To get circularly symmetric radiation pattern, the elements on the same circle are fed with the same magnitude. The numerical investigations show that the obtained beam shape is very close to the desired one with almost no ripples on the flat top. The final antenna design show acceptable performance regarding the impedance matching, the axial ratio and the sidelobe level over the operating bandwidth of the array.