A total of 32% of those quizzed said they would vote Yes if the referendum were held today while 47% said they would vote No. A further 20% were undecided and 1% indicated they would not vote.
One in seven Scots said they believe independence would make them better off financially while 38% thought it would leave them worse off.
The Angus Reid Public Opinion poll of 1,003 people was published in the Scottish Mail on Sunday.
The Scottish Government last week agreed to change the question it will put to voters in the independence referendum after concerns were raised that its preferred version could be biased towards a Yes vote.
First Minister Alex Salmond had proposed to ask: "Do you agree that Scotland should be an independent country?"
But the independent elections watchdog, the Electoral Commission, said using the phrase "Do you agree" was commonly felt "to be biased towards a Yes outcome".
The Scottish Government has accepted the commission's recommendation that the question should instead be: "Should Scotland be an independent country? Yes/No."
Subject to the approval of the Scottish Parliament, this is now likely to be the question put to people in the referendum which is due to take place in autumn next year.
Today's poll put the question "Should Scotland be an independent country?" to those it questioned and asked how they would vote if the referendum were held now.
Forty-seven per cent said they would vote No, 32% would vote Yes and 20% said they were undecided. One per cent indicated they would not vote.
Respondents were also asked: "Thinking of your own financial position, do you think independence will leave you better off, make no difference, or leave you worse off?"
In response, 14% said they would be better off, 38% worse off, 27% said it would make no difference and 21% said they were not sure.
The poll emerged on the same day as two leading businessmen gave their latest views on Scotland's future and the Yes and No campaigns.
Jim McColl, chairman and chief executive of Clyde Blowers, said Scottish independence would be tantamount to a "management buy-out" from the UK.
Mr McColl, who has previously indicated his support for independence, wrote: "While Westminster policies may work for London, they are not working for Scotland, for our economy or our society.
"A different approach is needed if we are to make Scotland the kind of country we all know it can and should be."
He continued: "We have a Government responsible for economic policy whose focus is not growth in Scotland but rather London and the south-east of England. That tells me Scotland is a nation in desperate need of a well-planned and thought-through management buy-out...
"There is so much opportunity in Scotland's future if we choose to claim it.
"A Yes vote in 2014 will give us the flexibility to choose the policies suited to Scotland regardless of who is elected to government at Westminster in 2015."
Meanwhile, entrepreneur Sir Tom Hunter said Scotland is facing a choice between a "leap in the dark or staying with a moribund status quo".
"Never, in my view, has such a factual void filled such an important debate," he said.
He went on: "No campaigners are digging themselves one enormous hole if they believe that a dual 'status quo' and 'scare them to death about independence message' will work.
"As Labour found to its cost in the last Scottish election, trying to scare Scots into submission is a recipe for getting what you never thought was possible: an SNP majority in the Scottish Parliament. Is it next step independence?
"Surely the No campaigners will have the intelligence to bring forward an agenda for Scotland that says tomorrow's going to be better than today for you in the United Kingdom?
"They need to spell out their agenda for Scotland's growth and prosperity to show just how much better it's going to be.
"Likewise, Salmond, one of the most talented politicians of his generation, and his cabinet must also move away from obfuscating the issues, the costs, the EU membership, and on to a clearly defined and costed programme for independence in 2014. So come on Alex, what's the vision? Where are the facts? Let's hear about the costs?"