In this paper, a Ku-band corrugated feed horn antenna for a Cassegrain reflector is designed and optimized. The horn dimension parameters are optimized so that it has a radiation pattern with a specific beamwidth which would illuminate the sub-reflector of the Cassegrain antenna with the desired taper. It is also required that the horn must have low S11 parameter and low cross-polarization levels. Multi-objective particle swarm optimization is performed to optimize the horn dimensions to meet these requirements. The radiation characteristics of the optimized horn are analyzed using computer simulation. The far-field radiation pattern of the Cassegrain reflector for the optimized feed horn is also discussed and compared with the case of an unoptimized horn.