In order to remove the restrictions on the number of antennas resulting from limited resources on satellites, the key components of the tri-band reflective antenna—Frequency Selective Surface(FSS) based sub-reflectors are studied. Firstly, the basic architecture of the tri-band reflective antenna system is summarized, then the hyperboloid type band-pass all-metal FSS as the sub-reflector is selected. By using the Floquet principle and Finite Element method, Ansys HFSS is chosen as the analysis tool to simulate and design. The results show that the insert loss is less than 0.3 dB, the amplitude difference between the two modes is less than 0.2 dB and the phase difference is less than 2.5°. The out-band rejection is better than 25.9 dB. Finally, the sub-reflector is fabricated and the performance is tested. The test results are in good agreement with the simulation results, which provides technical support for the tri-band reflective shared-aperture antenna system.