Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has precipitated multiple variants resistant to therapeutic antibodies. In this study, 12 high-affinity antibodies were generated from convalescent donors in early outbreaks using immune antibody phage display libraries. Of them, two RBD-binding antibodies (F61 and H121) showed high-affinity neutralization against SARS-CoV-2, whereas three S2-target antibodies failed to neutralize SARS-CoV-2. Following structure analysis, F61 identified a linear epitope located in residues G446-S494, which overlapped with angiotensin-converting enzyme 2 (ACE2) binding sites, while H121 recognized a conformational epitope located on the side face of RBD, outside from ACE2 binding domain. Hence the cocktail of the two antibodies achieved better performance of neutralization to SARS-CoV-2. Importantly, these two antibodies also showed efficient neutralizing activities to the variants including B.1.1.7 and B.1.351, and reacted with mutations of N501Y, E484K, and L452R, indicated that it may also neutralize the recent India endemic strain B.1.617. The unchanged binding activity of F61 and H121 to RBD with multiple mutations revealed a broad neutralizing activity against variants, which mitigated the risk of viral escape. Our findings revealed the therapeutic basis of cocktail antibodies against constantly emerging SARS-CoV-2 variants and provided promising candidate antibodies to clinical treatment of COVID-19 patients infected with broad SARS-CoV-2 variants.