Binding of the glucagon peptide to the glucagon receptor (GCGR) triggers the release of glucose from the liver during fasting; thus GCGR plays an important role in glucose homeostasis. Here we report the crystal structure of the seven transmembrane helical domain of human GCGR at 3.4 Å resolution, complemented by extensive site-specific mutagenesis, and a hybrid model of glucagon bound to GCGR to understand the molecular recognition of the receptor for its native ligand. Beyond the shared seven transmembrane fold, the GCGR transmembrane domain deviates from class A G-protein-coupled receptors with a large ligand-binding pocket and the first transmembrane helix having a 'stalk' region that extends three alpha-helical turns above the plane of the membrane. The stalk positions the extracellular domain (~12 kilodaltons) relative to the membrane to form the glucagon-binding site that captures the peptide and facilitates the insertion of glucagon's amino terminus into the seven transmembrane domain.