In this study, Fusion Driven Subcritical Spent Fuel Burner Reactor (FDS-SFB), designed by the Frontier Development of Science Team (FDS Team) in the first decade of this century, has been neutronically modeled to compare the effect of using the thorium fuel cycle, instead of the uranium fuel cycle, on the transmutation of long-lived hazardous radwaste (including 241Am, 243Am, 244Cm, 237Np, 238Pu, 241Pu, 242Pu). Furthermore, the neutronic spectrum of the different parts of the FDS-SFB, and the variation of the effective multiplication factor (keff) of the system have been also investigated to study effects of changing the fuel cycle. For these purposes, SuperMC code has been applied for the simulations and performing the Monte Carlo and Monte Carlo-deterministic coupling calculations. ENDF/B-VII neutron cross-section library was used for applying needed cross-sections. The spent fuel used in the modeling had been discharged from a standard, 33,000 MWD/MTU, Pressurized-Water Reactor (PWR). After ten years of the FDS-SFB operation it was found that, for all of the loaded long-lived radwaste, the thorium fuel cycle had a much better efficiency in the transmutation process. The Monte Carlo-deterministic calculations indicated that the final mass differences between the transmuted radwaste i.e. 241Am, 243Am, 244Cm, 237Np, 238Pu, 241Pu, and 242Pu, in both uranium and thorium fuel cycles were 582.3 kg, 51.2 kg, 48.2 kg, 611.6 kg, 427.2 kg, 1320.3 kg, and 357.4 kg, respectively. Considering the total amount of the radwaste loaded in the FDS-SFB, the thorium fuel cycle, with a 3398 kg difference, had considerably better efficiency than the uranium fuel cycle in the incineration of the loaded long-lived radwaste.