A design procedure for a dual feed network is presented to produce a circular polarized matched antenna involving eight design parameters with associated constraints. Determination of such design parameters has been made possible by utilizing a multiobjective genetic algorithm (MGA) approach. The conditions for circular polarization and impedance matching were the objective functions employed in the MGA. The associated constraints were the lengths and characteristic impedance values of the feed network. The return loss and axial ratio for a 5.8 GHz antenna were investigated and good agreement was obtained between simulated and practical measurements.