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We present a new evolutionary design method using genetic local search (GLS) algorithm to obtain broad/dual-band characteristics for circular polarization (CP) slot antennas. By employing this computer-aided design (CAD) technique, optimal or near-optimal impedance and axial-ratio bandwidths for a given operating frequency can be achieved without using the trial and error method. In our method, several key parameters were first investigated, and their effects on both the input impedance and the axial-ratio were obtained by simulation. Different local search procedures used in the GLS algorithm were then developed. The proposed design technique was evaluated by designing antennas using different slot shapes: the ellipse, the equilateral triangle, and the square. These antenna prototypes were constructed and measured to provide validation of the design method.