One major limitation of neutralizing antibody-based COVID-19 therapy is the requirement of costly cocktails to reduce antibody resistance. We engineered two bispecific antibodies (bsAbs) using distinct designs and compared them with parental antibodies and their cocktail. Single molecules of both bsAbs block the two epitopes targeted by parental antibodies on the receptor-binding domain (RBD). However, bsAb with the IgG-(scFv) 2 design (14-H-06) but not the CrossMAb design (14-crs-06) increases antigen-binding and virus-neutralizing activities and spectrum against multiple SARS-CoV-2 variants including the Omicron, than the cocktail. X-ray crystallography and computational simulations reveal distinct neutralizing mechanisms for individual cocktail antibodies and suggest higher inter-spike crosslinking potentials by 14-H-06 than 14-crs-06. In mouse models of infections by SARS-CoV-2 and the Beta, Gamma, and Delta variants, 14-H-06 exhibits higher or equivalent therapeutic efficacy than the cocktail. Rationally engineered bsAbs represent a cost-effective alternative to antibody cocktails and a promising strategy to improve potency and breadth.