The antenna is an important component in a radio communication system. Two kinds of antennas, transmitting and receiving antennas, are designed for use in a radio amateur satellite communication system. This thesis introduces the basic theory about antennas, the numerical technique Method of Moments, and wire grid models. It gives the design process for the downlink and uplink antennas, which are used for the satellite communication system. It implements a 2.4 GHz reflector antenna with a helix feed to realize the downlink, and a 435 MHZ 13 turns helix antenna for uplink. It also gives the measured total performance, and provides the computer simulation model.