Cetorhinicola acanthocapax Beveridge & Campbell, 1988 is redescribed based on adult specimens collected from a basking shark Cetorhinus maximus (Gunnerus) off the east coast of New Zealand. Both the mature and gravid segments are described for the first time, and the first scanning electron micrographs of the armature and scolex microtriches are provided. Novel features include the opening of the vagina anterior to the cirrus-sac and the extension of the vagina anterior to the cirrus-sac. Pectinate microtriches are present on the anterior quarter of the pars pedunculus scolecis scattered between filiform microtriches; the bothrial margins are covered with tridigitate microtriches, while the adherent surface of the bothria have pectinate microtriches. The additional morphological features described are consistent with a close association between Cetorhinicola Beveridge & Campbell, 1988 and the Eutetrarhynchoidea Guiart, 1927.