Backing for a Yes vote in September's referendum has fallen to 35%, while 54% said they would vote No, a YouGov poll for The Times said.
A further 10% said they were undecided, while 2% said they would not vote.
Without undecided voters or those who would not vote, the results were 39% for Yes, and 61% for No.
The results represent a slight decrease in support for independence, and a slight increase in backing for a No vote compared with the last YouGov poll for the newspaper in March.
Commenting on the results, Better Together campaign director Blair McDougall said: "This poll is a major setback to Alex Salmond's negative and divisive campaign.
"The more people think about the consequences of breaking up the UK for jobs, pensions and public services, the more they are saying No Thanks to separation.
"There will be no let-up from our campaign over the summer. We will be working hard for every vote until the polls close on September 18.
"We have a positive vision for Scotland that is winning over swing voters. We can have the best of both worlds for Scotland - a strong Scottish Parliament, with the guarantee of more powers, backed up by the strength, security and stability of being part of the larger UK. Only separation puts that at risk."
The poll also questioned people about whether they thought Scotland would be economically better or worse off under independence.
It found that 27% believed the country would be better off, 49% believed it would be worse off, 11% said there would be no difference and 13% did not know.
Meanwhile, 17% said they believed they would be personally financially better off under independence, 43% said worse off, 23% said no difference and 17% did not know.
YouGov interviewed 1,206 Scottish adults between June 25 and 29.