A two-arm spiral antenna printed on a finite-sized dielectric substrate backed by an infinite-sized conducting plane is analyzed using the finite-difference time-domain method (FDTDM). The antenna is fed by a vertical probe located at the center of the antenna. The antenna height above the ground plane is 0.147 wavelength. The FDTDM analysis reveals that the antenna forms an elliptically polarized conical beam. Based on this investigation, two parasitic elements are introduced near the vertical feed probe to obtain a circularly polarized conical beam. It is found that the current on the vertical feed probe is approximately 180 out of phase with the currents on the two parasitic elements. This results in a reduction in the radiation from the feed probe, with a corresponding improvement in the axial ratio. The frequency response of the antenna with the parasitic elements is also calculated. The angle of maximum radiation is approximately θmax54 for a bandwidth of m 6.2% (0.982f to 1.044f). Within this frequency band, the axial ratio is less than 3 dB, and 0 0 the gain is approximately 3.2 dBi.