The union, along with the Unite union, is in dispute with the Offshore Contractors Association (OCA) over pay.
The GMB said it was time for the OCA and its client employers to get around the table and find a solution.
A ballot of Unite members working offshore failed to reach the threshold needed to take strike action over pay conditions.
The OCA was unavailable for comment.
“GMB has long been saying that our members have got to the stage where enough is enough and this ballot result clearly sends a message to the OCA and their clients that they are sick to the back teeth of being down the pecking order in terms of the industries priorities.
“GMB members have played their part over the past few years seeing thousands of job losses and pay freezes and quite rightly want the offshore industry to recognise the sacrifices they have made.
“We have written to our members and to the employers today setting out the ballot results in full and will now consult on the next steps.”