Nuclear Fuel Security Act This bill establishes new programs and expands existing programs to increase domestic supplies of certain types of low-enriched uranium. First, the Department of Energy (DOE) must establish a program to increase the production of certain types of low-enriched uranium by U.S. nuclear energy companies. Second, DOE must expand the existing American Assured Fuel Supply Program to ensure the availability of certain types of domestically produced uranium in the event of a supply disruption. Third, DOE must establish a demonstration program to make certain types of low-enriched uranium available from its inventories, stockpiles, or allies to meet the needs and schedules of advanced nuclear reactor developers until such time that commercial enrichment and deconversion capability for the uranium exists in the United States at a scale sufficient to meet future needs.