The concept of the liquid Li17Pb83 and Helium gas dual-cooled Fuel Breeding Blanket (FBB) for the Fusion-Driven sub-critical System (FDS) is presented and analyzed. Taking self-sustaining tritium (TBR ＞1.05) and annual output of 100 kg or more fissile 239Pu (FBR＞0.238) as objective parameters, and based on the three-dimensional Monte Carlo neutron-photon transport code MCNP/4A, a neutronics-optimizated calculation of different cases was carried out and the concept is proved feasible. In addition, the total breeding ratio ( BR = TBR + FBR ) is listed corresponding to different cases.