The SARS-CoV-2 virus is more transmissible than previous coronaviruses and causes a more serious illness than influenza. The SARS-CoV-2 receptor binding domain (RBD) of the spike protein binds to the human angiotensin-converting enzyme 2 (ACE2) receptor as a prelude to viral entry into the cell. Using a naive llama single-domain antibody library and PCR-based maturation, we have produced two closely related nanobodies, H11-D4 and H11-H4, that bind RBD (KD of 39 and 12 nM, respectively) and block its interaction with ACE2. Single-particle cryo-EM revealed that both nanobodies bind to all three RBDs in the spike trimer. Crystal structures of each nanobody-RBD complex revealed how both nanobodies recognize the same epitope, which partly overlaps with the ACE2 binding surface, explaining the blocking of the RBD-ACE2 interaction. Nanobody-Fc fusions showed neutralizing activity against SARS-CoV-2 (4-6 nM for H11-H4, 18 nM for H11-D4) and additive neutralization with the SARS-CoV-1/2 antibody CR3022.