Mitochondrial complex I (also known as NADH: ubiquinone oxidoreductase) contributes to cellular energy production by transferring electrons from NADH to ubiquinone coupled to proton translocation across the membrane(1,2). It is the largest protein assembly of the respiratory chain with a total mass of 970 kilodaltons(3). Here we present a nearly complete atomic structure of ovine (Ovis aries) mitochondrial complex I at 3.9 angstrom resolution, solved by cryo-electron microscopy with cross-linking and mass-spectrometry mapping experiments. All 14 conserved core subunits and 31 mitochondria-specific supernumerary subunits are resolved within the L-shaped molecule. The hydrophilic matrix arm comprises flavin mononucleotide and 8 iron-sulfur clusters involved in electron transfer, and the membrane arm contains 78 transmembrane helices, mostly contributed by antiporter-like subunits involved in proton translocation. Supernumerary subunits form an interlinked, stabilizing shell around the conserved core. Tightly bound lipids (including cardiolipins) further stabilize interactions between the hydrophobic subunits. Subunits with possible regulatory roles contain additional cofactors, NADPH and two phosphopantetheine molecules, which are shown to be involved in inter-subunit interactions. We observe two different conformations of the complex, which may be related to the conformationally driven coupling mechanism and to the active-deactive transition of the enzyme. Our structure provides insight into the mechanism, assembly, maturation and dysfunction of mitochondrial complex I, and allows detailed molecular analysis of disease-causing mutations.