This study presents the time-dependent analyses of transmutations of long-lived fission products (LLFPs) and medium-lived fission products (MLFPs) occurring in thermal reactors in a conceptual helium gas-cooled accelerator-driven system (ADS). In accordance with this purpose, the CANDU-37 and PWR 15 × 15 spent fuels are separately considered. The ADS consists of LBE-spallation neutron target, subcritical fuel zone, and graphite reflector zone. While the considered ADS is fueled with the spent nuclear fuels extracted from each thermal reactor without the use of additional fuel, fission products extracted from same thermal reactor are also placed into transmutation zone in graphite reflector zone. The LLFP transmutation performance of the modified ADS is analyzed by considering three different spent fuels extracted from the thermal reactors. Spent fuels are extracted from CANDU-37 in case A, from PWR-15 × 15 in case B, and from CANDU-37 fueled with mixture of PWR 15 × 15 spent fuel and 46% ThO2 in case C. The LBE target is bombard with protons of 1000 MeV. The proton beam power is assumed as 20 MW, which corresponds to 1.24828·1017 protons per second. MCNPX 2.7 and CINDER 90 computer codes are used for the time-dependent burn calculations. The ADS is operated under subcritical mode until the value of keff increases to 0.984, and the maximum operation times are obtained as 3400, 3270, and 5040 days according to the spent fuel cases of A, B, and C, respectively. The calculations bring out that in the modified ADS, LLFPs and MLFPs, which are extracted from thermal reactors, can be transformed to stable isotopes in significant amounts along with energy production.