The Lerwick-registered Njord capsized in the North Sea, around 100 nautical miles west of Stavanger.
The Norwegian Joint Rescue Co-ordination Centre (NJRCC) launched a rescue operation after the alarm was raised about 1:40pm on Sunday.
Rescuers found the eight crew standing on the keel of the capsized vessel Njord.
Three people were winched into a search and rescue helicopter and were flown to Haukeland University Hospital in Bergen where one of them subsequently died.
The other five people were picked up by an offshore vessel, the Olympic Challenger, which was five nautical miles away.
A spokesman for the JRCC said the trio rescued by helicopter had all inhaled diesel and one was later pronounced dead.
A NJRCC spokesman said: “When we were alerted we sent out resources and found eight people standing on the keel of the capsized fishing vessel.
“Three were taken into a search and rescue helicopter and five people were picked up by boat after we issued a Mayday relay.”
The NJRCC said the vessel was registered in Lerwick. However, the trawler reportedly left Peterhead at the weekend.
According to reports from the BBC, the JRCC said there was no radio contact with the stricken 24m vessel, but they were automatically alerted by the trawler's emergency position-indicating radio beacon, which activated when it started taking on water.
No details regarding the man who died or the crew members involved in the incident have been released.
The owner of the Olympic Challenger, an oil industry offshore vessel, which had responded to the Mayday relay issued by rescue services calling on vessels nearby to assist, sent out a small boat and rescued five of the crew who were in the water, before giving them warm clothes, food and drink.
The owner of the vessel Stig Remøy said: "The crew has done a great job, where the quick action taken has clearly saved lives."
The Norwegian Coastguard confirmed it had also received the alert and a helicopter had been sent.
The boat was built in 1992 as the Guardian Angell, and became the Courageous in 2015.
A new Courageous was delivered in March last year.