Today, 29 percent are in favour of Nato membership, 5 percent more than in December 2004, and 53 percent are against it.
The figures come from a new poll by the Sifo polling firm carried out for the Svenska Dagbladet newspaper ahead of the Nato summit in Bucharest which starts on Wednesday.
In 2004, 59 percent of poll respondents were against Swedish membership in Nato.
The Moderate Party is the only political party in which those in favour of Nato membership outnumber those against, 46 percent versus 42 percent.
Similarly, the Liberal Party is supports entry into Nato, but among its voters, 48 percent are against and 36 percent are in favour.
Among Social Democratic voters, 22 percent are in favour, while 56 percent are against. In 2004, 67 percent had negative attitudes toward Swedish membership in Nato.
Meanwhile, 83 percent of Left Party voters and 75 percent of Green Party voters counted themselves among the naysayers.
Sifo asked 1,000 people of they thought that Sweden should join the Nato defence alliance. The interviews were conducted between March 25th and March 27th.