Global Health Security Act of 2020 This bill establishes a permanent, presidentially appointed position to manage outbreak response efforts. Specifically, the bill establishes the role of Special Advisor for Global Health Security who shall (1) serve as the President's principal advisor on global health security and global health emergencies (2) coordinate U.S. efforts to carry out global health security activities, and (3) convene the Global Health Security Interagency Review Council. The bill establishes such council to provide policy guidance to participating agencies on global health security matters and to facilitate the implementation of the existing Global Health Security Agenda. The Special Advisor must also develop a strategy to advance global health security and other specified policy objectives and coordinate a whole-of-government approach to the implementation of such strategy. In addition, the Department of State must coordinate and facilitate interagency, multi-sectoral activities outside of the United States in response to a declared global health emergency.