The lead–bismuth eutectic (LBE) can be easily activated by neutron radiation to produce the radionuclide 210Po. It is therefore necessary to establish an effective method to remove vaporized polonium in the cover gas to prevent its release into the air in scenarios of reactor maintenance and coolant leakage accidents. This paper presents a SiO2 nanofiber membrane prepared based on the electrostatic spinning and calcination process. The SiO2 nanofiber membrane had the advantages of good flexibility, high-temperature resistance, and corrosion resistance. In the trapping experiments, the SiO2 nanofiber membrane filters showed excellent filtration performance at 300~400 °C, and the filtration efficiencies for Te, Pb, and Bi could reach 99%, 99%, and 98%, respectively. Proper filtration temperature and gas flow rate are important to maintain high filtration efficiency. After five cycles, the SiO2 nanofiber membrane filter still exhibited excellent cycle-use performance. In the density functional theory (DFT) calculations, PbPo and PbTe had strong interactions with amorphous SiO2, having adhesion energies of −2.96 to −2.83 eV/molecule.