A new species of cestode, Mathevotaenia niuguiniensis n. sp. (Anoplocephalidae: Linstowiinae), is described from the hydromyine rodent Parahydromys asper (Thomas) in Papua New Guinea. This is the third species of the genus reported from the Australasian region. The new species differs from all congeners in rodents by having an elongate cirrus-sac, which crosses the osmoregulatory canals and extends into the medulla, compared with a short, ovoid cirrus-sac which does not penetrate into the medulla in congeners. It differs from the known Australian species, M. antechini (Beveridge, 1977) and M. nyctophili (Hickman, 1954), found in dasyurid marsupials and bats respectively, by lacking a complex of anastomosing osmoregulatory canals in each segment. A list of all known species of Mathevotaenia Akumyan, 1946, their host genera, host families and geographical distribution is provided. New combinations proposed in this report are: M. dipodomi (Bienek & Grundmann, 1973) n. comb. (transferred from Schizorchodes Bienek & Grundman, 1973), M. genettae (Ortlepp, 1937) n.comb., M. mephitis (Skinker, 1935) n. comb., M. pedunculata (Chandler, 1952) n. comb., M. wallacei (Chandler, 1952) n. comb. (transferred from Oschmarenia Spasskii, 1951) and M. oedipomidatis (Stunkard, 1965) n. comb. (transferred from Paratriotaenia Stunkard, 1965).