7,088,045 Swedes and residents are registered to vote and by Saturday 12 percent (844,968) had taken the chance to pre-vote in the election.
The Swedish candidates are fighting for 18 seats in the parliament - one less than in the previous election in 2004.
According to several recent opinion polls the Pirate Party stands to claim a seat in the parliament for the first time as it enjoys a boost in popularity for its focus on the future of the internet and integrity issues.
The party was largely invisible in the polls prior to the convictions of the four backers of file-sharing site The Pirate Bay on April 17th.
A poll on April 29th recorded their support at 5 percent and an average of the three most recent polls indicates support of 7.7 percent.
The election is shaping up as one for the smaller parties with the Green party, as well as the Liberals, enjoying recent boosts in the polls at the cost of the dominant Social Democrats and Moderates.
In 2004 the Social Democrats claimed the most mandates with five, followed by the Moderates with four, June List with three, Liberal and Left parties with two and the Centre, Green and Christian Democrat parties with one apiece.
Recent surveys indicate that as many as one in four Swedes are unaware that there is an election on Sunday. Centre party leader Maud Olofsson underline on Sunday the importance of party leaders in raising awareness of EU issues.
"It is a challenge to us all to talk about EU questions even between elections," Olofsson said to news agency TT.
Recent election news has focused on the issue of private contributions to political party coffers following the confirmation of reports of a one million kronor ($128,000) donation to Feminist Initiative (Feministiskt initiative - FI) candidate Gudrun Schyman from former Abba great Benny Andersson.
Schyman has long complained over election procedures, in particular the distribution of ballot paper which she argues benefits the major parties at the cost of the likes of Fi.
Schyman claimed Andersson shares her democratic concerns over voting procedure amid media speculation that his funding was intended to deflect attention from the file-sharing and copyright debate.
Sweden has only a voluntary arrangement for the disclosure of party contributions and the European Council has in the past directed criticism at Sweden for the lack of disclosure and warned of corruption, according to Dagens Nyheter on Saturday.
The polling stations will remain open until 9pm on Sunday and preliminary results will begin to filter through an hour later.
Aside from Sweden, 18 other European Union countries are holding elections to the EU parliament on Sunday.