An array composed of spiral elements, each having a small number of turns, is numerically analyzed. The spiral elements are circularly arrayed above a ground plane and are excited by a single vertical feed wire. As the number of the spiral elements increases, the copolarization component of the radiation becomes omnidirectional. The maximum variation in the copolarization component as a function of azimuth angle is 0.8 dB for four spiral elements. Attention is also paid to an improvement in the axial ratio. A technique of using parasitic wires around the feed wire is presented. Calculations show that, when the distance between the feed wire for four spiral elements and the parasitic wires is appropriately chosen, the axial ratio is improved. The 3-dB axial ratio frequency bandwidth evaluated in the maximum beam direction is found to be 10%. Within this bandwidth, the gain is more than 5 dB.