Urgent action is needed to stop the Balearic sheerwater being drowned in fishing lines and nets, say scientists.
The bird breeds in the Balearic Islands, sometimes stopping off in British waters as it migrates north.
Research shows the global population is not sustainable in the long term. There are about 3,000 breeding pairs left.
The main threat to the bird is becoming entangled in fishing gear, according to findings published in the Journal of Applied Ecology.
Other risks include hunting by the likes of cats and other small mammals.
Prof Tim Guilford of the Department of Zoology at the University of Oxford is co-researcher on the study.
He told BBC News: “The survival of adults from one year to the next and especially of young adults is much lower than we thought.
“The species is unsustainable – it is on the road to extinction.”
Night fishing
Estimates suggest about half of deaths in adult birds are due to accidental capture in fishing lines and nets.
Fishing on the seabed is a particular risk as birds can become entangled and drown when lines are immersed, say researchers in the UK and Spain.
Changes such as setting fishing gear at night when the bird does not dive “could make a massive difference”, said Prof Guilford.
“The science shows just how serious the problem is, but also that there is a technically simple solution – the setting of demersal long-lines at night,” he added.
The Balearic shearwater (Puffinus mauretanicus) is one of the rarest seabirds in the world.
The seabird is classified as critically endangered on the IUCN Red List of species.
It breeds on cliffs and small islets and lays only one egg.