An elderly man is missing and it's feared he's gone overboard from a cruise ship due to dock in Sydney after a 13 day cruise around New Zealand.

Carnival Australia says a thorough search of the Sun Princess has failed to find the 84-year-old man, who was reported missing very early this morning.

The Sun Princess was due to dock in Sydney today but is now retracing its path.

The Rescue Co-ordination Centre in Canberra is also helping - and says the search area is quite small as they have a fairly good idea of where the incident occurred.