It represents another drop in enthusiasm for a second vote, from 43% last June to 32% in September.
The poll also showed that a majority (51%) do not want another independence vote held within the next few years.
Writing in the Sunday Times, former senior SNP adviser Kevin Pringle admitted that many people viewed the prospect of another independence referendum 'with weariness and distaste', and that it would bring 'unpleasant attitudes' to the fore.
Scottish Conservative leader Ruth Davidson said:
"Scotland is now sending a very clear message to Nicola Sturgeon - we don't want your second referendum.
"As her own former spokesman says today, many people view the prospect of such a vote with 'weariness' and 'distaste' because of the 'unpleasant attitudes' it will bring to the fore.
"He is absolutely right. People desperately want the SNP to focus on the day job, not yet more division and uncertainty.
"Nicola Sturgeon should now act on behalf of all of Scotland, not just the SNP, by ditching her unwanted and unnecessary plans.
"Only by doing so can we pull together as a country and confront the challenges we all face."