This paper presents the core design studies of a sodium-cooled fast reactor (SFR) and a sodium-cooled accelerator-driven system (ADS) for a two-stage fast-spectrum fuel cycle to enhance uranium resource utilization and reduce nuclear waste generation. The first-stage SFR starts with low-enriched uranium (LEU) fuel and operates with the recovered uranium and plutonium from the discharged fuels and natural uranium at equilibrium. The recovered minor actinides (MAs) are sent to the second-stage ADS, where they are burned in an inert matrix fuel form. Reference core designs were developed for a 1000-MW(thermal) LEU-fueled breakeven fast reactor (LEUBFR) and an 840-MW(thermal) MA-fueled ADS blanket. The SFR starts with uranium fuel with a 235U enrichment of 13.6% and reaches a fuel-breakeven core after 14 cycles with an 18-month cycle length. At the equilibrium state, one ADS supports 37 fast reactors. Using the performance parameters of SFR and ADS, the proposed two-stage fuel cycle was evaluated. The results of the equilibrium cycle analysis showed that the two-stage fuel cycle option could achieve a high reduction in waste generation because of the continuous recycling of the plutonium and MAs. In addition, the mass flow data showed that this two-stage fuel cycle option increases the efficiency of natural uranium utilization and reduces the nuclear waste generation compared to the conventional two-stage fuel cycle options based on thermal and fast-spectrum systems.