The Yagi-Uda antennas have a wide range of applications ranging from radio broadcasting to passive radar systems. In this study, a Yagi-Uda antenna was developed to be used as a receiving antenna in an FM based passive radar system operating at 92 MHz. Antenna calculations were made with traditional formulas and then genetic algorithms and particle swarm optimization were applied to determine the most appropriate parameters. Finally, the design and analysis of the antenna was done in FEKO environment. The gain of the developed antenna has been optimized as 11.3308 dBi and the VSWR value is 1.0307.