The mu-opioid receptor (mu OR) is a G-protein-coupled receptor (GPCR) and the target of most clinically and recreationally used opioids. The induced positive effects of analgesia and euphoria are mediated by mu OR signalling through the adenylyl cyclase-inhibiting heterotrimeric G protein G(i). Here we present the 3.5 angstrom resolution cryo-electron microscopy structure of the mu OR bound to the agonist peptide DAMGO and nucleotide-free G(i). DAMGO occupies the morphinan ligand pocket, with its N terminus interacting with conserved receptor residues and its C terminus engaging regions important for opioid-ligand selectivity. Comparison of the mu OR-G(i) complex to previously determined structures of other GPCRs bound to the stimulatory G protein G(s) reveals differences in the position of transmembrane receptor helix 6 and in the interactions between the G protein alpha-subunit and the receptor core. Together, these results shed light on the structural features that contribute to the G(i) protein-coupling specificity of the mu OR.