Three new species of carnivorous sponges of the genus Abyssocladia (Demospongiae, Cladorhizidae), A. kanaconi, A. microstrongylata and A. mucronata, are described from the bathyal zone of the Tropical Southwestern Pacific, south of New Caledonia. They were collected in 2016 and 2019 during the KANACONO and KANADEEP 2 expeditions of the Tropical Deep-Sea Benthos program of the French Museum National d’Histoire Naturelle. A new record is reported for the cladorhizid Cercicladia australis Rios, Kelly & Vacelet, 2011, and the spicules of the holotype of the type species of Abyssocladia, A. bruuni Lévi, 1964 are illustrated.