The Ipsos MORI survey, conducted on behalf of Oxfam, showed more than half of all Scots – 52 % – feel the present tax system is not fair compared with 37% who believe it is fair.
Among those who think the wider system of taxation is unfair are 61% of the country's richest people.
Those working part-time (57%), those not in work (61%) and those living in the most deprived parts of the country (61%) are also more likely to be critical of the tax system.
The findings came as the Scottish Tories said they may fight the next Holyrood election on a pledge to cut the basic rate of income tax by at least 2p.
Under the new Scotland Act, the Scottish Parliament will be responsible for raising a portion of basic rate income tax from 2016.
The head of Oxfam Scotland, Judith Robertson, said: "This survey shows Scots want a fairer system. At the moment, the poorest Scots are taxed more heavily than the richest. In 2010/11, the poorest fifth of people paid around 38.2% of their income in tax – the richest fifth paid 33.6%.
"Without a robust and progressive tax system we can't deliver the public services people need, nor can we tackle growing inequality."