The Scotpulse survey for STV found that 59 per cent of those polled think that Brexit will be bad for Scotland.
24 per cent think that leaving the European Union, which is expected to be officially concluded within the next two years, will be a good thing.
It comes as both sides of the campaign reflect on the one year anniversary of the vote by 52 per cent of voters in the UK to back leaving the EU.
Scotland, one of two constituent countries in the UK to go against the national result, voted Remain by a margin of 62 to 38 per cent.
10 per cent of Leave voters in Scotland would change their vote if there was another EU referendum, while just 3 per cent of Remain voters would switch sides, the poll found.
Holding another referendum on the final terms of Brexit wasn’t backed by any of the three largest parties in Westminster at the General Election held earlier this month.
The Liberal Democrats under outgoing leader Tim Farron, had pledged to offer voters a ‘final say’ on the deal, but there was external (and internal) criticism of that position.
STV’s poll also found that there was no a majority for the Scottish Government’s preferred outcome on another referendum on independence due to Brexit.
17 per cent of those surveyed agreed with Nicola Sturgeon that there should be a referendum on independence after Brexit.
A further 13 per cent backed another vote on the constitution in Scotland, but they wanted it held before Brexit, bringing the total in favour to 30 per cent.
In contrast, 48 per cent of those polled believe that there shouldn’t be another referendum at all, while 22 per cent say it depends on what happens with Brexit.