It comes as British voters go to the polls in the UK today to decide whether the country should remain a member of the European Union or leave.
The survey of 700 Austrians was taken by Peter Hajek Opinion Strategies, who found that 38% of them were in favour of an Austrian EU referendum and 55% were against the idea.
It's been 20 years since the country held its first EU referendum and voted to enter the Union.
Over two decades late, the biggest supporters for holding another Austrian referendum are those who vote for the right-wing and EU-skeptic Freedom Party.
Those who are most against the idea of holding a new Austrian referendum support the Green party. The majority of supporters of the other parties are also against it.
“A clear majority of Austrians are against a referendum about Austria withdrawing from the EU,” said Peter Hajek, who led the survey.
“This part of the population probably don't want that possibility at all, because you don't know how it could develop.”
Of those surveyed, 28% said they would want Austria to leave the EU although the clear majority are in favour of staying.
“Fifty-three percent are for staying in the EU and only 28% are for an exit. But there are still 15% who are undecided,” said Hajek.
The results of this survey compares to one carried out in 2014 that suggested one quarter of Austrians would support the country leaving the EU.
That survey also found support for the EU was high at around 67%.