The study was carried out by the SOM Institute at the University of Gothenburg. Some 50 percent of those who participated said they wanted to phase out the power source.
When the same study was carried out in 2011, following the Fukushima disaster, 44 percent of respondents said they weren't keen on nuclear power. By contrast, in the 2007 study just 31 percent of respondents said they wanted to phase it out.
The figures follow the same trend of public opinion reacting to a disaster said the university's professor of political science Sören Holmberg.
"After the accidents at Chernobyl (1986) and Three Mile (1979) the support for nuclear power declined initially," Holmberg told the TT news agency.
Following the Chernobyl meltdown the number of Swedes surveyed, who wanted to phase out nuclear power, reached a record high of 75 percent in the 1986 survey.
In 1980 the Swedish government pledged to phase out its fleet by not replacing or building new reactors when the old ones were decommissioned.
However, in 2010 Parliament revoked the moratorium on new reactors. It's estimated that 35 percent of all electricity in the country is produced by the plants.
At present Sweden has 10 nuclear reactors at three plants, the largest one being in Gothenburg.
Professor Holmberg added that Sweden needed to emulate countries like Germany, Switzerland and Italy by phasing out the controversial power source.
He said that the country should consider alternative sources of energy, such as wind power.
"There isn't the same need for us to invest in nuclear power any longer," he told TT.
Last year a leading Social Democrat politician, Magdalena Andersson, said that nuclear power should be "abolished."
Sweden's first nuclear plant opened in 1972.