This research proposes a novel dual-band (2.45/5.80 GHz) omnidirectional circularly polarized (CP) biconical antenna with double-circular parasitic parallelepiped elements for wireless local area network (WLAN) applications. The proposed dual-band CP antenna scheme consisted of a biconical radiating structure surrounded by inner-and outer-circular parallelepiped elements that convert linearly polarized electric fields into CP fields. Simulations were performed to optimize the antenna parameters, and an antenna prototype was fabricated and experiments were conducted. The measured impedance bandwidths (IBWs) were 44.4% (1.84 -2.89 GHz) and 4.56% (5.73 -5.99 GHz) for the lower-(2.4 GHz) and upper-frequency (5.80 GHz) bands, respectively. The corresponding 3-dB axial ratio bandwidths (ARBWs) were 11.22% (2.27 -2.54 GHz) and 10.49% (5.6 -6.2 GHz). The radiation patterns of the dual-band antenna scheme were omnidirectional left-hand circular polarization, with the measured antenna gains of 3.2 dBic and 8.5 dBic at 2.45 and 5.80 GHz, respectively. The simulated and measured results were reasonably agreeable. Despite the narrow IBW and ARBW for the upper-frequency band, the bandwidths adequately covered the target upper frequency band, rendering the proposed CP omnidirectional biconical antenna scheme operationally suitable for WLAN applications. Furthermore, the novelty of this research lies in the use of a biconical radiating structure augmented with double-circular parasitic parallelepiped elements to realize circular polarization for dual-band WLAN applications.