Global Health Security Act of 2020 This bill directs the President to create the Global Health Security Agenda Interagency Review Council to implement the Global Health Security Agenda, an initiative launched by nearly 30 nations to address global infectious disease threats. The council's responsibilities include (1) providing policy recommendations on agenda-related goals, objectives, and implementation; (2) helping federal agencies with implementation; and (3) reviewing the progress and challenges in achieving U.S. commitments, including assistance to help other countries meet agenda targets. The bill also directs the federal agencies involved with the agenda to prioritize its implementation and to take certain steps to achieve that goal. The President shall also appoint a U.S. Coordinator for Global Health Security to coordinate and report on the interagency process for responding to global health security emergencies.