Fresh figures show that 33 percent of Swedes consider Nato membership to be a good idea, up from 28 percent in a similar survey from April last year.
A further 47 percent of Swedes are against the idea, a considerable drop from the 56 percent who were against it in April.
The survey was carried out by pollsters Ipsos for the Dagens Nyheter newspaper.
David Ahlin at Ipsos said that the Swedes have long had a steady opinion of Nato since the early nineties, but that a new trend was emerging.
"The support has doubled if you compare the figures today to those from 20 years ago," he said.
Nato (which stands for the North Atlantic Treaty Organisation) is an international organisation that includes various European countries as well as the United States and Canada.
It was formed in 1949, after the end of the Second World War.
Nato's aim is to ensure that its members don't fight each other, rather that they work together to safeguard security and cooperate on defence and security issues.
If diplomatic efforts fail, it has the capacity to organise and carry out joint defence operations when urgent military action is needed, for example in Afghanistan.
The organisation has recently expanded its presence in the Baltics, as tensions continue in the region as a result of the Ukraine crisis.
Crucially, member states are obliged to come to the aid of fellow members if they are subject to a military attack.
Sweden already has strong links to Nato and takes part in joint training exercises with Nato troops as part of the Partnership for Peace programme. Some argue this makes Sweden a Nato member in all but name, while others point out that Sweden isn't covered by security guarantees.