An upward-facing antenna unit for the Global Navigation Satellite System Reflectometry (GNSS-R) system is designed. To address the issues of low cross-polarization purity and large phase center offset in traditional antennas, a dual U-slot loading method is applied in the design, significantly enhancing both the cross-polarization isolation and phase center stability. Based on the method, a stacked structure is used to achieve dual-band functionality. The antenna operates in the GPS L1 (Beidou B1) and L5 (Beidou B2a) frequency bands. Simulation results show that the antenna's return loss S11 bandwidths are approximately 120 MHz and 21 MHz, with the axial ratio at the center frequency being less than 3 dB. The phase center stability in the L5 (B2a) band is about 1.2 mm.