Oligomeric and protofibrillar aggregates formed by the amyloid-β peptide (Aβ) are believed to be involved in the pathology of Alzheimer’s disease. Central to Alzheimer pathology is also the fact that the longer Aβ42 peptide is more prone to aggregation than the more prevalent Aβ40. Detailed structural studies of Aβ oligomers and protofibrils have been impeded by aggregate heterogeneity and instability. We previously engineered a variant of Aβ that forms stable protofibrils and here we use solid-state NMR spectroscopy and molecular modeling to derive a structural model of these. NMR data are consistent with packing of residues 16 to 42 of Aβ protomers into hexameric barrel-like oligomers within the protofibril. The core of the oligomers consists of all residues of the central and C-terminal hydrophobic regions of Aβ, and hairpin loops extend from the core. The model accounts for why Aβ42 forms oligomers and protofibrils more easily than Aβ40.