In this paper, a dual-band RF wireless power transfer (WPT) system with a shared-aperture dual-band Tx array antenna for 2.4 and 5.8 GHz is proposed. The final configuration of the Tx array, which is made up of 2.4 GHz right-handed circular polarization (RHCP) patches and 5.8 GHz RHCP patches, is derived from the optimization of 2.4 and 5.8 GHz thinned arrays, ultimately to achieve high transmission efficiency for various WPT scenarios. The dual-band RF WPT Tx system including the Tx array antenna and a Tx module is implemented, and Rx antennas with a 2.4 GHz patch, a 5.8 GHz patch, and a dual-band (2.4 and 5.8 GHz) patch are developed. To validate the proposed dual-band RF WPT system, WPT experiments using a single band and dual bands were conducted. When transmitting RF wireless power on a single frequency (either 2.482 GHz or 5.73 GHz), the received power according to the distance between the Tx and Rx and the position of the Rx was measured. When the distance was varied from 1 m to 3.9 m and the transmitted power was 40 dBm, the received power value at 2.482 GHz and 5.73 GHz were measured and found to be 24.75−13.5 dBm (WPT efficiency = 2.985−0.224%) and 19.25−6.8 dBm (WPT efficiency = 0.841−0.050%), respectively. The measured results were in good agreement with the calculated results, and it is revealed that the transmission efficiency when wireless power is transmitted via beam-focusing increases more than that with conventional beam-forming. Furthermore, the dual-band WPT experiment proves that 2.482 GHz beam and 5.73 GHz beams can be formed individually and that their wireless power can be transmitted to a dual-band Rx or two different Rx.