The fusion of 6He with 206Pb has been studied at energies close to and below the Coulomb barrier. The experiment was carried out at the Dubna Radioactive Ion Beams complex of FLNR, JINR. The 6He beam intensity was about 5 x 10(6) pps, the maximum energy being 60.3+/-0.4 MeV. The yield of the 210Po isotope, produced in the 2n-evaporation channel, demonstrates an extremely large enhancement of the sub-barrier fusion cross section as compared with the 4He+208Pb reaction. This enhancement is most likely due to the mechanism of "sequential fusion" with an intermediate neutron transfer from 6He to the Pb nucleus with positive Q values.