Galeus priapus sp. nov. is described from specimens collected on the slopes of the seamounts and ridges of southern New Caledonia and Vanuatu. It is the first Galeus species recorded in these areas. G. priapus is characterised by the presence of a conspicuous crest of enlarged denticles on the dorsal caudal margin, the absence of similar crest on ventral caudal margin, and extremely long and slender claspers in adult males that extend posteriorly to the anal-fin origin. The body coloration, which is plain greyish brown with large dark blotches on dorsal and caudal fins and their bases, closely resembles its sibling G. gracilis, a northern Australian and Indonesian species. An identification key to Indo-Pacific Galeus species is provided.