The COVID-19 pandemic caused by nonstop infections of SARS-CoV-2 has continued to ravage many countries worldwide. Here we report that suramin, a 100-year-old drug, is a potent inhibitor of the SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) and acts by blocking the binding of RNA to the enzyme. In biochemical assays, suramin and its derivatives are at least 20-fold more potent than remdesivir, the currently approved nucleotide drug for treatment of COVID-19. The 2.6 Å cryo-electron microscopy structure of the viral RdRp bound to suramin reveals two binding sites. One site directly blocks the binding of the RNA template strand and the other site clashes with the RNA primer strand near the RdRp catalytic site, thus inhibiting RdRp activity. Suramin blocks viral replication in Vero E6 cells, although the reasons underlying this effect are likely various. Our results provide a structural mechanism for a nonnucleotide inhibitor of the SARS-CoV-2 RdRp.