Neutralizing antibodies that target the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein are among the most promising approaches against COVID-19^,. A bispecific IgG1-like molecule (CoV-X2) has been developed on the basis of C121 and C135, two antibodies derived from donors who had recovered from COVID-19. Here we show that CoV-X2 simultaneously binds two independent sites on the RBD and, unlike its parental antibodies, prevents detectable spike binding to the cellular receptor of the virus, angiotensin-converting enzyme 2 (ACE2). Furthermore, CoV-X2 neutralizes wild-type SARS-CoV-2 and its variants of concern, as well as escape mutants generated by the parental monoclonal antibodies. We also found that in a mouse model of SARS-CoV-2 infection with lung inflammation, CoV-X2 protects mice from disease and suppresses viral escape. Thus, the simultaneous targeting of non-overlapping RBD epitopes by IgG-like bispecific antibodies is feasible and effective, and combines the advantages of antibody cocktails with those of single-molecule approaches.