National Green Bank Act of 2019 This bill establishes a U.S. Green Bank to finance climate change mitigation and adaptation projects at the state and local level by capitalizing regional, state, and municipal green banks. The Department of the Treasury must issue green bonds to provide the bank with (1) an initial capitalization of $10 billion; and (2) additional capitalization, upon the bank's request, of no more than $50 billion in aggregate at any one time. The bill also establishes in the Treasury a revolving Green Bank Establishment Fund.