A five-year trial reintroduction of the species into a forest in Argyll at Knapdale is due to end next month. Ministers will then have to decide whether beavers should become a permanent feature in the landscape, although a decision is not expected until next year.
A YouGov poll commissioned for the Scottish Beaver Trial of 1652 adults found three in five (60%) support the reintroduction of beavers to Scotland, with this level of support broadly similar across all ages.
It found 5% oppose, 30% neither support nor oppose with the rest undecided.
In addition, of those who had been aware of the Scottish Beaver Trial prior to the research (355 re-spondents), 74% were supportive of beavers being reintroduced to Scotland.
The trial, a partnership led by the Scottish Wildlife Trust and the Royal Zoological Society of Scotland, hosted by Forestry Commission Scotland, is the first formal trial reintroduction.
Between May 2009 and September 2010 16 Eurasian beavers were released into Knapdale Forest near Lochgilphead, around lochs and waterways, in five distinct family groups.
Five died, eight are missing but there are now 17 at Knapdale, eight born in Scotland.
Simon Jones, project manager of the Scottish Beaver Trial, said: "It is really positive to see majority support for the reintroduction of beavers to Scotland."
The Scottish Government decided in 2012 to allow the estimated 100 animals to roam free in rejecting an option to cull them. Ministers will also decide what to do with them next year.