Some 67 percent of 1,000 Swedes questioned June 25-28 said they wanted to vote on the treaty in a referendum, while 29 percent said parliament should decide. Four percent said they had no opinion, the Sifo poll showed.
The survey was commissioned by the June List, a Eurosceptic party not represented in parliament, which published the results on its website.
A large majority of those questioned, 64 percent, said a 2003 Swedish referendum vote to keep the Swedish krona and reject the euro was “a good decision”.
Twenty-nine percent said the result was a bad decision and seven percent said they had no opinion.
The opposition Green and Left parties called last month for a referendum to be held on the EU treaty, which is aimed at streamlining EU decision-making.
Sweden’s centre-right government, headed by Prime Minister Fredrik Reinfeldt, has indicated that it plans to ask parliament to vote on the text.
Parliament was scheduled to do so in 2005, but the French and Dutch rejections of the EU constitution put the process on hold indefinitely.