The Panelbase survey for The Sunday Times puts backing for remaining in the bloc at 65 per cent, up from 61 per cent in January.
It also found that 50 per cent of Scots think Brexit will leave Scotland’s economy weaker, while 24 per cent think it will strengthen it and 26 per cent believe it will make little difference.
Scotland voted in favour of Remain by 62 per cent to 38 per cent in the 2016 referendum.
Despite the rise in support, Panelbase found minority backing for an independent Scotland reapplying to the EU, with 48 per cent in favour of such a move.
• READ MORE: Poll: Support for independence sees boost to 46%
A further 32 per cent were opposed to a return in the event of independence, while 20 per cent favour neither option.
Support for independence itself stands at 43 per cent, down two percentage points on the Yes vote in the 2014 referendum, while opposition is up two points at 57 per cent, the survey found.
SNP MP Kirsty Blackman said: “It is no surprise that support for our EU membership is growing in Scotland, as we begin to see the reality of the huge damage that an extreme Tory Brexit will do to people’s jobs, businesses, incomes, living standards, and our wider economy.”
Scottish Conservative deputy leader Jackson Carlaw said: “This poll makes clear that there is simply no appetite for the further instability and division that a second referendum would cause.”
He added: “It is time the SNP dumped the grievance politics and worked constructively with the UK government to deliver the best Brexit deal for us.”
Panelbase surveyed 1,021 adults online between August 31 and September 7.