HIV-1 uses a diverse N-linked-glycan shield to evade recognition by antibody. Select human antibodies, such as the clonally related PG9 and PG16, recognize glycopeptide epitopes in the HIV-1 V1–V2 region and penetrate this shield, but their ability to accommodate diverse glycans is unclear. Here we report the structure of antibody PG16 bound to a scaffolded V1–V2, showing an epitope comprising both high mannose–type and complex-type N-linked glycans. We combined structure, NMR and mutagenesis analyses to characterize glycan recognition by PG9 and PG16. Three PG16-specific residues, arginine, serine and histidine (RSH), were critical for binding sialic acid on complex-type glycans, and introduction of these residues into PG9 produced a chimeric antibody with enhanced HIV-1 neutralization. Although HIV-1–glycan diversity facilitates evasion, antibody somatic diversity can overcome this and can provide clues to guide the design of modified antibodies with enhanced neutralization.