Potent neutralizing antibodies (nAbs) against SARS-CoV-2 are a promising therapeutic against the ongoing COVID-19 pandemic. However, the continuous emergence of neutralizing antibody escape variants makes it challenging for antibody therapeutics based on monospecific nAbs. Here, we generated an IgG-like bispecific antibody (bsAb), Bi-Nab, based on a pair of human neutralizing antibodies targeting multiple and invariant sites of the spike receptor binding domain (RBD): 35B5 and 32C7. We demonstrated that Bi-Nab exhibited higher binding affinity to the Delta spike protein than its parental antibodies and presented an extended inhibition breadth of preventing RBD binding to angiotensin-converting enzyme 2 (ACE2), the cellular receptor of SARS-CoV-2. In addition, pseudovirus neutralization results showed that Bi-Nab improved the neutralization potency and breadth with a lower half maximum inhibitory concentration (IC50) against wild-type SARS-CoV-2, variants being monitored (VBMs) and variants of concern (VOCs). Notably, the IgG-like Bi-Nab enhanced the neutralizing activity against Omicron variants with potent capabilities for transmission and immune evasion in comparison with its parental monoclonal antibody (mAb) 32C7 and a cocktail (with the lowest IC50values of 31.6 ng/mL against the Omicron BA.1 and 399.2 ng/mL against the Omicron BA.2), showing evidence of synergistic neutralization potency of Bi-Nab against the Omicron variants. Thus, Bi-Nab represents a feasible and effective strategy against SARS-CoV-2 variants of concern.