The Panelbase survey of 1,020 voters for the Sunday Times found 51 per cent are not supportive of a second referendum within the next year or two.
First Minister Nicola Sturgeon has said another ballot on the issue is highly likely after the UK voted to leave the European Union despite a majority vote to remain north of the border.
The poll, carried out last week, found support for a second independence referendum before Brexit has fallen from 43 per cent following the vote last June to just 27 per cent.
While 61 per cent said they believe the UK should remain in the EU, 39 per cent want to leave, with support for Brexit at 35 per cent of those who voted Yes in the 2014 independence referendum.
Around a third (31 per cent) of voters oppose Scotland applying to join the EU in the event of independence, compared to 48 per cent who are supportive and 21 per cent who do not know.
Overall, the poll found support for independence is slightly up on the 2014 result at 46 per cent, with the No vote at 54 per cent.