The worldwide spread of COVID-19 highlights the need for an efficient approach to rapidly develop therapeutics and prophylactics against SARS-CoV-2. The SARS-CoV-2 spike protein, containing the receptor-binding domain (RBD) and S1 subunit involved in receptor engagement, is a potential therapeutic target. We describe the development of a phage-displayed single-domain antibody library by grafting naive complementarity-determining regions (CDRs) into framework regions of a human germline immunoglobulin heavy chain variable region (IGHV) allele. Panning this library against SARS-CoV-2 RBD and S1 subunit identified fully human single-domain antibodies targeting five distinct epitopes on SARS-CoV-2 RBD with subnanomolar to low nanomolar affinities. Some of these antibodies neutralize SARS-CoV-2 by targeting a cryptic epitope located in the spike trimeric interface. Collectively, this work presents a versatile platform for rapid antibody isolation and identifies promising therapeutic anti-SARS-CoV-2 antibodies as well as the diverse immogneic profile of the spike protein.