The site, opposite the Rarotonga International Airport, is the resting place of mostly foreigners and includes many New Zealanders and Australians.
TV One's Seven Sharp programme reported tonight at least three Kiwi graves were among several that had washed away over the years.
Several other graves near the sea wall towards the back of the cemetery are also in danger of being ruined. Among those is a grave that belongs to a Kiwi expat, Brian Latchford .
Mr Latchford's family, from Invercargill, told Seven Sharp they wanted to see the cemetery looked after properly as theirs was not the only family who had a cherised loved one lying there.
The story follows ongoing controversy about the lack of maintenance at the cemetery, known to the locals as Brych Yard Cemetery.
In recent years, a "Save The Brychyard Cemetery" Facebook page has been set up to bring families of loved ones buried at the site together. It also encourages locals to help restore the graves.
The Cook Islands Government, which owns the cemetery, told the current affairs programme it would be carrying out an "immediate plan" to make sure graves were secured and would not be in danger of being washed away.