The survey by pro-independence group Progress Scotland found 63% of respondents see the country leaving the UK in future.
A total of 59% of those surveyed said they believe a second independence referendum is likely to take place within five years.
Progress Scotland managing director Angus Robertson said: “These polling results show the value of this research, showing that a majority of all respondents expressing an opinion believe that Scottish independence will happen and that an independence referendum will and should happen.
“Our particular focus is on people who are open-minded or undecided on independence, and our research indicates this is a fifth of the electorate.
“We have asked a series of interesting questions of this group covering the economy, governance, defence and security and Europe.
“This is just the beginning of research by Progress Scotland and we are very grateful of the support of thousands of subscribers who help fund our work.”
Other findings include keeping the pound as the national currency for the long-term in an independent Scotland has the support of 47% of the 2,000-plus respondents.
Switching to a Scottish currency in the short-term was only favoured by 6%.
Pamela Nash, chief executive of Scotland in Union, said: “Yet again this opinion poll has backfired for the SNP.
“It has revealed the strength of support for saving the pound, with not even a quarter of those undecided about independence backing the SNP leadership’s blueprint for a new currency.
“By remaining in the UK we can keep our pound, protect mortgages, pensions and salaries, grow our economy without extra red tape for businesses, and use a stable currency backed by the strength of the UK’s central bank and 30 million taxpayers.
“That’s why so many people who voted Yes in 2014 have changed their minds and now want to stay in the UK.”
An SNP spokesman said: “We welcome this poll which shows that 63% of people think Scotland will become an independent country, and that Brexit is driving up support for independence.
“Scotland’s wishes have been completely ignored by Westminster throughout the Brexit process, and it is clear we are not treated as an equal partner in the UK.”
Scotland voted to remain part of the UK by 55% to 45% during the 2014 Scottish independence referendum.
The research group has previously found 21% of respondents who took part in that ballot have changed how they would vote or they are no longer sure.