Most oceanic plateaux are massive basaltic volcanoes. However, the structure of these volcanoes, and how they erupt and evolve, is unclear, because they are remote and submerged beneath the oceans. Here we use multichannel seismic profiles and rock samples taken from Integrated Ocean Drilling Program core sites to analyse the structure of the Tamu Massif, the oldest and largest edifice of the Shatsky Rise oceanic plateau in the north-western Pacific Ocean. We show that the Tamu Massif is a single, immense volcano, constructed from massive lava flows that emanated from the volcano centre to form a broad, shield-like shape. The volcano has anomalously low slopes, probably due to the high effusion rates of the erupting lavas. We suggest that the Tamu Massif could be the largest single volcano on Earth and that it is comparable in size to the largest volcano in the Solar System, Olympus Mons on Mars. Our data document a class of oceanic volcanoes that is distinguished by its size and morphology from the thousands of seamounts found throughout the oceans.