A total of 32% of those quizzed said they would vote Yes if the referendum were held today, while nearly a half said they would vote No.
The Scottish Government last week agreed to change the question it will put to voters in the referendum.
First Minister Alex Salmond had proposed: "Do you agree that Scotland should be an independent country?"
But the Electoral Commission, said "Do you agree" was commonly felt "to be biased towards a Yes outcome".
The Scottish Government accepted the recommendation that the question should instead be: "Should Scotland be an independent country?"