COVID-19 Serving the Homeless by Expanding the List of Tenant Eligible Residences Act of 2020 or the SHELTER Act of 2020 This bill expands the housing choice voucher program for low-income families and authorizes additional vouchers. Specifically, the bill authorizes incremental housing vouchers for families that were unsheltered or living in shelters as of the March 13, 2020, presidential emergency declaration relating to COVID-19 (i.e., coronavirus disease 2019). Such vouchers may be used to rent an eligible housing unit under the existing program or to rent other types of housing, including recreation vehicles, hotel or motel rooms, and short-term rental units. Further, the bill waives certain requirements for receiving such assistance, such as requirements related to income verification and lease duration. The bill also authorizes additional incremental vouchers under the existing housing choice voucher program.