Glucagon and insulin maintain blood glucose homeostasis and are used to treat hypoglycemia and hyperglycemia, respectively, in patients with diabetes. Whereas insulin is stable for weeks in its solution formulation, glucagon fibrillizes rapidly at the acidic pH required for solubility and is therefore formulated as a lyophilized powder that is reconstituted in an acidic solution immediately before use. Here we use solid-state NMR to determine the atomic-resolution structure of fibrils of synthetic human glucagon grown at pharmaceutically relevant low pH. Unexpectedly, two sets of chemical shifts are observed, indicating the coexistence of two β-strand conformations. The two conformations have distinct water accessibilities and intermolecular contacts, indicating that they alternate and hydrogen bond in an antiparallel fashion along the fibril axis. Two antiparallel β-sheets assemble with symmetric homodimer cross sections. This amyloid structure is stabilized by numerous aromatic, cation-π, polar and hydrophobic interactions, suggesting mutagenesis approaches to inhibit fibrillization could improve this important drug.